{ "metadata": { "name": "LinearModels" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": "# Linear Basis Function Models for Regression and Classification #\n\nBased on Bishop ch 3 and ch 4.\n\n### Included in this workbook ### \n1. Code for a generic linear model with custom basis functions \n2. Using the model for regression \n3. Using the model for classification \n4. Demo of how regularization affects generalization \n\n## Linear Basis Function Model ##\nThis is a generic linear model, and it currently has one dimensional output. So it's suited for one-dimensional regression or binary classification. It supports using custom basis functions and training with either gradient descent or the normal equation. " }, { "cell_type": "code", "collapsed": false, "input": "%pylab inline\n\nclass LinearModel(object):\n \"\"\"\n A generic linear regressor. Uses nonlinear basis functions, can fit with\n either the normal equations or gradient descent\n \"\"\"\n \n def __init__(self, basisfunc=None):\n \"\"\"\n Instantiate a linear regressor. If you want to use a custom basis function,\n specify it here. It should accept an array and output an array. The default\n basis function is the identity function.\n \"\"\"\n self.w = array([])\n self.basisfunc = basisfunc if basisfunc is not None else self.identity\n \n def identity(self, x):\n #identity basis function - for linear models in x\n return x\n \n def basismap(self, X):\n #return X in the new basis (the design matrix)\n Xn = zeros((X.shape[0], self.basisfunc(X[0,:]).shape[0]))\n for i, xi in enumerate(X):\n Xn[i,:] = self.basisfunc(xi)\n return Xn\n \n def fit_gd(self, X, y, itrs=100, learning_rate=0.1, regularization=0.1):\n \"\"\"\n fit using iterative gradient descent with least squares loss\n itrs - iterations of gd\n learning_rate - learning rate for updates\n regularization - weight decay. Greated values -> more regularization\n \"\"\"\n \n #first get a new basis by using our basis func\n Xn = self.basismap(X)\n \n #initial weights\n self.w = uniform(-0.1, 0.1, (Xn.shape[1],1))\n \n #now optimize in this new space, using gradient descent\n print 'initial loss:', self.loss(X,y)\n \n for i in range(itrs):\n grad = self.grad(Xn, y, regularization)\n self.w = self.w - learning_rate*grad\n \n print 'final loss:', self.loss(X,y)\n \n def grad(self, X, y, reg):\n \"\"\"\n Returns the gradient of the loss function with respect to the weights.\n Used in gradient descent training.\n \"\"\"\n return -mean((y - dot(X, self.w)) * X, axis=0).reshape(self.w.shape) + reg*self.w\n \n def fit_normal_eqns(self, X, y, reg=1e-5):\n \"\"\"\n Solves for the weights using the normal equation. \n \"\"\"\n Xn = self.basismap(X)\n #self.w = dot(pinv(Xn), y)\n self.w = dot(dot(inv(eye(Xn.shape[1])*reg + dot(Xn.T, Xn)), Xn.T) , y)\n \n def predict(self, X):\n \"\"\"\n Makes predictions on a matrix of (observations x features)\n \"\"\"\n Xn = self.basismap(X)\n return dot(Xn, self.w)\n \n def loss(self, X, y):\n #assumes that X is the data matrix (not the design matrix)\n yh = self.predict(X)\n return mean((yh-y)**2)\n ", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "Populating the interactive namespace from numpy and matplotlib\n" } ], "prompt_number": 165 }, { "cell_type": "markdown", "metadata": {}, "source": "Let's test it out. First, let's make some basis functions:" }, { "cell_type": "code", "collapsed": false, "input": "def fourier_basis(x):\n #use sine waves with different amplitudes\n sins = hstack(tuple(sin(pi*n*x)) for n in arange(0,1,0.1))\n coss = hstack(tuple(cos(pi*n*x)) for n in arange(0,1,0.1))\n return hstack((sins, coss))\n\ndef linear_basis(x): #includes a bias!\n return hstack((1,x))\n\ndef polynomial_basis(x): #degree 10\n return hstack(tuple(x**i for i in range(10)))\n\ndef sigmoid_basis(x): #offset sigmoids\n return hstack(tuple((1+exp(-x-mu))**-1) for mu in arange(-9,9,0.5))\n\ndef heavyside_basis(x): #offset heavysides\n return hstack(tuple(0.5*(sign(x-mu)+1)) for mu in arange(-9,9,0.5))\n", "language": "python", "metadata": {}, "outputs": [], "prompt_number": 177 }, { "cell_type": "markdown", "metadata": {}, "source": "Now we'll generate some data." }, { "cell_type": "code", "collapsed": false, "input": "#generate some data\nX = arange(-8, 8, 0.1).reshape((-1,1))\ny = sin(X) + randn(X.shape[0],X.shape[1])*0.3\nscatter(X, y)\n", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 179, "text": "" }, { "metadata": {}, "output_type": "display_data", "png": 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HsWNnULFiZUyefDHfJwV37FiLTp16Q6udAoNBAr2+N1atOgCRSIH582cV9+GUSb/8shRt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\nMWZD/j/ThkvZIWFGwQAAAABJRU5ErkJggg==\n", "text": "" } ], "prompt_number": 179 }, { "cell_type": "markdown", "metadata": {}, "source": "Linear basis, without a bias." }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel()\nmodel.fit_normal_eqns(X, y, reg=0.1)\nXn = arange(-8, 8, 0.05).reshape((-1,1))\nyh = model.predict(Xn)\nscatter(X, y)\nplot(Xn, yh)\ntitle('Linear basis, no bias')\nshow()", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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GDBjM3r0HqFChHF9+OZ4nnujG/v1lSEjoidG4gqCg5fz11y4182UOmzx5MkOH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\nO3S6ycDHGI0P8MorU10dVo2zatUXmEy18fGpQ4sWkSQmJpZ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"text": "" } ], "prompt_number": 161 }, { "cell_type": "markdown", "metadata": {}, "source": "Linear basis, with a bias. Since the data are centered, this won't be any different then the above. We'll see an example later where the bias is important." }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=linear_basis)\nmodel.fit_normal_eqns(X, y, 0.1)\nXn = arange(-8, 8, 0.05).reshape((-1,1))\nyh = model.predict(Xn)\nscatter(X, y)\nplot(Xn, yh)\ntitle('Linear Basis, with bias')\nshow()", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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S15tMfhw6tINFi5Zw9OgZmjSpzcsvD3F6b8H8aPr06Ywdu424uOXAGaABcAxo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\nvcjImAME8+GH07l6dSqffvqBs0OrEGrVqsWAAYP45pv+WCy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"text": "" } ], "prompt_number": 160 }, { "cell_type": "markdown", "metadata": {}, "source": "We can obviously see that the data are from a sine wave. Using a sinusoidal basis..." }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=fourier_basis)\nmodel.fit_normal_eqns(X, y, 0.1)\nXn = arange(-8, 8, 0.05).reshape((-1,1))\nyh = model.predict(Xn)\nscatter(X, y)\nplot(Xn, yh)\ntitle('Fourier basis')\nshow()", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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pdBnVrVv4cCaM6fbuJWrQgOgVw++YNZb0LdiqVURDhhRc7u8fQELhtzlJ5glx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\nwMXFBdnZ2di2bRumTJlyz+MUTfqCIFRcXbq0Q1zc58jOfgqAK7Ta2Xj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"text": "" } ], "prompt_number": 181 }, { "cell_type": "markdown", "metadata": {}, "source": "Sine is an analytic function. We should be able to approximate it with a polynomial, right?" }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=polynomial_basis)\nmodel.fit_normal_eqns(X, y, 0.1)\nXn = arange(-8, 8, 0.05).reshape((-1,1))\nyh = model.predict(Xn)\nscatter(X, y)\nplot(Xn, yh)\ntitle('Polynomial basis')\nshow()", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ADQJHCTSkWu3MQ4cOiR1mhrKaO/NNppWSfs4qXtyDwP6UP+JkajQ+XLlyZbpyQ4aMolrd\nOuUPfC8FoRjPnTuX9wEXESNHfkG1ug2BRwSuUhDKcefOnab1jx49oq1tccrl0whsoiDU4Ndf+5rW\nBwYGsk+fwRwwYDgvXbokxikUSg0atCbwv5TPy+8EepgumAADlUoVY2JixA4zQ1LSl5Ak9+3bR0Fw\noEYzgFptQ9at24yJiYnpytnaliQQbPoDl8kmcfLkqXkfcBFRunQVAhdTJZR5HDRohGn9ggULqFJ9\nlGr9XWo09iTJgIAACoITgQUEfqBG48CLFy+KdSqFyldfTaFa3Y5APIE9BMoQiEn5HZyhRmOXb++4\nspo7pQe5hVTLli1x6dIJ/PxzY/z+++c4fnwfzM3N05UTBC2AMNOymVkYrKy0eRhp0WKcJvRv07KZ\n2d9wcvp36lCSIFM/LFQAMNbX+vr+hLi4+QBGAZiA2NgJmDNncV6EXej5+k5CixaWUCrtoVR2RalS\nGmg0XrCy6gxBaIf161dCJpOJHWaOkB7kFnEbN27CwIFjER//KczM7sPe/jCuXTsDBwcHsUMrlE6c\nOIGWLT9AUlIvKJXPYWV1BkOG9EVCgh7t2rWCm5sbqlSpg+joL0BWgCB8h+HDvTF37izUquWDixe/\nANA2ZW9L0aXLKWzb9ruYp1SoREVFATDO7X369GmEhYWhVq1aKFeunMiRvZ40tLIky/7880/4+++G\nra0Vhg8fJiX8XHbr1i3s3r0bJPHzz7/g+fP60Ok8oFYvQf361fH4cTiiomLg4uKCHj3a4YsvPoNc\nLsdvv63CqFEzERe3EEA8VKohKFu2HBITdWjVqhnmzZsFlUr11uNLChcp6UskBYSfnx/Gjz+GhIRN\nMFbhNAJQAsBwmJntQ/Hiu3DjxnkIgmDa5tdff8PChatgMOhx584tJCTMBlAdavW3aNvWClu3rhbn\nZCSiyfMeuQMHDoSTkxOqVq362jKjR4+Gh4cHvLy8cOnSpeweUpLKiRMn0KFDb7Rs2Q3+/v5ihyPJ\ngpiYGOj1JVOWHgG4DWADgPeRlPQjXrxQY+bMmdiyZQtiY2MBAIMHD8SVK39i1KiPIJN1ADAIQC3E\nx6+Bv/9mGAwGUc6loJAuLHMg6X/88ccICAh47fo9e/bgzp07CAoKwi+//IJPPvkku4eUpDh9+jRa\ntvwAu3Z548CBD9Cnz0hs3rxF7LAkmdSmTRuYm68BsAfAfQCJAPQpa28hJuY2fvrpGgYO/AVVqtRD\nRESEaVuVSgW5PCLV3iKhUJgXmoeNOS0kJAReXo2gVJrD2dkVhw4dEjsk8eREk6F79+6xSpUqGa4b\nNmwYN27caFouX748nzx5kq5cDoVSpPTpM5jAvFTN+3awZs1mpvUGA6nXixig5K0CAgLo7l6Djo7l\nWLJkxZQ+E+spk3kQmG363ZqbD+Xnn39l2i4qKoqlS1egmdlgAn4UhIqcPn2miGeSfxkMBrq6VqVc\n/j2BBAL7qdE4MDQ0VOzQckRWc2euN9kMCwtDqVKlTMslS5bEw4cPc/uwRYLx9y0DoAMwCcAk/P13\nEBYvDkK7doCVFWBmBpQqBYwaBYSGihuvJL1WrVohKOginj27i+Dgy5g4sSlat94OG5tkAA1M5XS6\nurh//7Fp2dLSEpcuncAXX7igf/9r+O23qZg8eaIIZ5D/hYeHIyzsAQyGCQAsALSAQtEQ586dEzs0\nUSjz4iD8Tz3a625BfX19TT97e3vD29s7F6Mq+EaOHAh//w8QF/c/GB8ErkBsrANGjpRj9uznWLvW\nETY2QFAQsHIlULMmMHcuMGCA2JFLMmJubm5K3CNGfI7ffpuLhISaAGIhCEvRosWwNOXt7Owwc+Z0\nESItWKysrGAw6ACEACgHIBHJyX/D0dFR3MDeUWBgIAIDA999Bzlxe/G26p0NGzaYlqXqnZwVGBhI\nuVxF4FmqqoARXLBgQbqyf/1Fli1L/vCDCIFKsiQuLo4dO/aiQmFOpdKCo0ePz7c9QguC+fMXURBK\nUqX6hFptTXbq1LvQvJ9ZzZ25fqXfsWNH+Pn5oVevXjh9+jRsbGzg5OSU24ctMt577z2o1daIjdWY\nXlMqn8HcPH1rqkqVgOPHgRYtAAsLYMyYvIxU8iYxMcDZs0B4OFCsGFCnjhr+/huQmJgIhUIBpTJP\nbsoLrdGjP0WdOjVw7tw5lC7dEh07dszWQ28SKKjPzLPdTr937944evQowsPD4eTkhGnTpiEpyTgG\n9bBhxtvRkSNHIiAgABqNBitXrkTNmjXTByK1039nTZqcw8mTCTAYbkKp/Av29v/DjRvnU7r8pxcS\nAtSvD6xfD/j45G2skrSePQO+/hrYvBmoWhVwcQHCwoAbN4D+/YFvvwWsrcWOUgIYq6kPHz6KVas0\niI31wB9/2IgdEgBpaOUiZ+dOY5XNL79sY8+eA/nZZ+MzrD77r0OHSGdn8unTPAhSkqFdu4y/g88/\nJ58/T7vuyRNy6FCyRAny8OGcOV5CQgKPHj3KwMBAxsfH58xOi4joaAPr1FlHmewe5fKbtLCozXXr\nNrx9wzyQ1dwp9cgtwKKigCpVgNWrgXd55j1+vPGqcv36HA9N8harVwNffQVs2gQ0afL6cgcOAB9+\nCCxfDmRnatbIyEjUr/8+Hj+WAZDByUmP06cPwd7e/t13WgQ8fgz4+QGLFukQExOI5OQmANQArkGl\naoyYmAjRZ9OS5sgtQr75xlg//66NnKZNM9Yj79qVo2FJUhgMBsyaNQcVK9ZH7do+pg5B69YBkyYB\nhw+/OeEDxt/vnj3A0KHAwYPvHstXX/kiJKQuoqPPIzr6HO7fb4Lx46e8+w4LufBw4LPPgMqVgZcv\ngalT90MQlsOY8AGgKgwGmgZoK1By4W7jneSjUAqEv/4iHR3JFy+yt5/9+0k3NzKDofYl2TRt2kwK\nQq2U2Zc2URAcuWrVX3RwIK9fT1v25s2b/OGHHzh//nw+e/Ys3b6OHCGdnMg7d94tliZN2hPYnqoj\n3/9Yv36rd9tZAWEwGHjkyBFu3ryZ9+/fz/R2u3aRxYqRI0YYq9lI8vbt21SrHVLmQjBQJlvM0qUr\n5IsWQFnNnfkm00pJP2s6dybnzMmZfbVpQ/7TwjMhIYE7duzgunXrGBYWljMHKGIOHTrEhQsX0tHR\nlcD5VIl2Ni0tI/jHH2nLnzx5khqNA5XK0bSw6EdHx9J8/Phxuv36+ZFeXu/2Bf3ll5OpVn9AIJGA\njipVN44d+9XbNyygkpOT2b59D2q1lWhp2ZkajQMPHjz41u1mzSJLliSPH0+/bsuWrVSrralUCixT\nphJv3bqVC5FnnZT0CyGDwcBjx45x/fr1vHXrFk+dMv5hxsXlzP6vXDFe2Tx6FMuqVetTq21ErbYb\nLS2L8cKFCzlzkELs4MGDrFnTm56eddiw4fvUaNypUg2nTGZP4FCqpH+BtWunzyZ16rxPYE2q+YzH\ncNy4L9OUSUxMZHKyge3akVOnZj3G+Ph4Nm/ekSqVPVUqBzZr1o5xOfUHlA9t27aNGk3tlC85EthP\nJ6dyb9zmxx9JT0/y0aPXl0lOTuarV6/yxRX+P6SkX8gYDAYOHDiCGo0bLS27Ua12ZNWqj7hsWfqy\nISEhbNWqK93carJPn8GMjIzM9HH69ydbtTpOlaoLAUPKB2UVq1dvkoNnU/icP3+eguBIYDOBbQS0\nBMJT3r9fCNgT8KNMtoZyeTD/+uteun24udUkcDrVl4Mf+/UbStJY7ePqWpUymYK2ti5cv/4oHRzI\ny5ezHqvBYGBYWBgfPnyYr5JWbvj5559pYTEi1XsaR4XC7LXnvWmTsRXcgwfknj17OHHi1/Tz8ysQ\nrZykpF/InDhxghqNK4HolD/e2wTCGBOTlKZcVFQUnZ1dqVDMIHCGFhaDWbdus0x/uG/eJNXqaAJz\nU31QbtHJyS03TqvQ+OKLrwhMNV3JA5VTvX8GqtWubN68NzWaSA4fvoE2Ni40N9ewXbsejIqKStnH\n1xQEHwKhBC5TEFy5fft26vV6uri4USZbQiCZwGFqNA78/vsINm1qHFBPkrGTJ09SEErQOP+zgXL5\nDFav3jjDsnfuGJ+PXbhAfv/9HAqCGwFfqtXtWLNmkwznls5PpKRfyGzatImWll1SJRJSofiG4eHh\nvHz5Mnfu3Ml79+5x3759tLJqkqqcniqVQ5bq5Rs0eEBz81kEHhFIorn5IHbr1j8Xz67gmzx5KhWK\n0SnveQwBJwJrCfgRsCKgYLlyG9msWRgFoXjKg8BIWlj0Zdeu/UiSOp2Ow4aNoaVlMdrZleKCBYtI\nkg8ePKBa7ZTmd29l1ZqbN2+jg8Njenj4sk+fwRnW/0vIhQsX08xMoLm5FT08qmf4MPfFi5esVCma\n06dHUK/X08xMnfLlSwLJ1GobcMeOHSJEn3lS0i9kgoKCUqoPLppuU83NXWlmZkOZzJ6C0IKC4MCp\nU32p1XqlXBGSQDTNzS35/L+9ft7g4kXS0vIVFQpLKhQWbNq0DV++fJmLZ1fw3b9/n9bWzpTLvyKw\ngCpVMVpaFiPgSOAmgTgCUbS3r01gYqoE/oBWVs5v3HdMTAzNzTUpV6vG36lGU5aNG7ekuflkAjFU\nKCayZElPRkdH59EZFyw6nY4vXrzI8I73zz//pIXFF1QoztPCwo5TpsygQmFOIMn0e9Jqe3LNmjUi\nRJ55UtIvhDZv3kKVyopy+VwqFIuoVLYnUCJV3fElqlRWrF69EVWqHgSWURCasE+fQVk+lo8PuWaN\nnrGxsblwJoXTvXv3OHLkOPbvP4x79+7lhAkTCfiaqniADQRcCXRI9bxkH8uUqfzWffv5LaEguFAQ\nPqJGU4G9e39MMzMNgXhTYrK09OauXbvy4EwLD4PBQGvrSjSOr08CjygIJVitWkOamw8nEEJgE7Va\nxyw19xSDlPQLqbg4PR0dkymXV0pJIh3S3ParVI68c+cOfX2/Zc+eA7lggR/17zCDyvbtZP36uXAC\nRchPP/1ElaprSoLXpyT8cAI1CLQlMJgqlR337t2bqf2dP3+ey5cv5/79+/ny5cuUpB+b6mrUm7t3\n787lsypcIiIiKJcvSfUZ0lGr7cSlS5eyffuetLUtwfLla/PkyZNih/pWUtIvZPR6PUNDQ7lqVTx9\nfEit1oHAHgIOBK6l/MFuoYNDqXdK8umPR5YpQ549m/3Yi5rr169z7ty5nD9/Pj08qlOp3E+FYgOB\nYilfALEEfqOFRXGuW7funY/TpUtfqtWtCGyjTHaL9vaTpDuzLHrwwECZLILAQQKraGx1pWbx4h4M\nCgoSO7wskZJ+IXLr1i0WL+5OQXChTHaU/fvv5fLlK1JaJXxAQE2ZzJZ2diV57ty5HDvujz8am3BK\nMu/gwYMUBAeam4+iWt2Zzs4tqNXG8YcfltLNrRrNzMYQOEul8muWKVOJT5484YABw1m5ckN269Y/\nSw9jdTodp06dQW/vjmzX7me6uiYxOTkXT64QGjWK7NnzIQXBloB1yvMXUiabRw+PGmKHlyVZzZ3S\ngGv5mIdHdQQHDwP5CYBkqNXuOHJkIxITE3H48BHY2tqgbdu2KFeuXI6Ot/78OeDhAdy/Lw3rm1nl\ny9fG7dtTAHQEAMjlB/Dee1ocPtwA4eHhGD58HC5fvo6KFT2xZMkcfPDBh7h2zR063QAolbtRsuQu\n3Lx5ASqVKkvHJYG6dYEpU4AOHXLhxAqhx4+NY+rcuAFs2bIQEyacQ0LC6pS1BsjlFoiLi4GFhYWo\ncWZWVnOnNDNDPqXX6xEcfA3k0JRXFJDJmuPSpUsYPnw4mjZtmqn9kMTu3bsRHBwMLy+vTE1B6egI\nNG8ObNwIDBv21uISAJGREQAqmJYNhsbw9JwLoAEcHBywdetq07q7d+/i5s070OmOAJBDr2+CFy8O\n4vz582jcuPFrj6HX6xEXFwcrKyvTazIZMHYsMG+elPQzQ6fTYfjwm6hQwYCQkER4enpCqfwFQDyM\ng6mdgVZrB3Nzc5EjzT3SKJv5lFKphJ1dCQCBKa/EQSY7iXLlymV6HyQxYMBw9Oo1CV9+GYR27QZi\n2rRZmdp20CBgxQrjzwkJCdi4cSOWL1+Ou3fvZuk8ioo2bVpCpZoI4DmAR1AodqF79wYZljUzM4PB\nkAQgKeXhfB0jAAAgAElEQVQVgox/493akiW/QKOxhr29CypVqoOHDx+a1nXrBty+DVy+nGOnUygl\nJSWhYcP2+N//SuHcuf14//0uePz4Kdq2rQWNpgYsLbtCEDpi3boV2ZpVK9/L8Qqmd5SPQsk3Dh06\nRAuL3lQorlOjKct+/YZmqfv85cuXKQilUjoNkcBjmptbMiIi4q3b6vXGCTxOn45lpUp1qNU2oyD0\np0bjwGPHjmXntAql2NhY9ujxEVUqB8pkjzllyvbXljUYDGzbthvV6tYEfqdK1Ys1azZhUlJShuVP\nnTqV8hwniICBCoUva9V6L02ZGTPIIUNy8owKn82bN9PCYnqqZrNXqdXa02AwMDAwkBs3bmRwcLDY\nYWZZVnNnvsm0UtLPWKdOsfz002s8d+4c4+PjefDgQQYEBLyxM86yZcvp4uJBS8tiNDevl6Zpp0ZT\nhlevXuWkSVPZoUMffvvtrNd2M//6a7Jp0wtUqTqn+qBsZfnytXPrdPO1hw8f8vjx42+cmez338nm\nzd++L51Oxxkzvmf79r351VeTGRMT89qy8+bNo4XFyFS/x1gqFOZpyjx6RNrYkFIfrddbsmQJZbLg\nVO9jIuVyZY60ehOTlPQLkago0tqaDA8nIyMjWb58TVpa1qGVVROWLOmZ4RAL/v7+FISyNA7gdSql\nKdofBOIpk/nR2dmVtWo1TenE9TvV6rZs1apzhncQwcH/jMfzXaoPSjDt7Uvz7t27HDRoBDt37seN\nGzflxdshqqVLl1OttqO1dT2q1XbctGlLhuVq1zaOx56TNm/eTI2mLgFdyu/gQIYjRnbqRC5fnrPH\nLkz8/YMJhBE4TCCCZmaj2KjR2+cU0Ol0nDTJl7Vq+bBTpz757m4gz5P+3r17Wb58ebq7u/P7779P\nt/7IkSO0srJi9erVWb16dX777bcZByIl/XR+/53s0MH485gx42lhMch0xa1UTspwXJw+fQYTWJQq\nSS+lUmlLuVzJChVqc8uWLdRqy6d0GiKBBKpUxXjv3r0MY6ha9QXNzYcSuEMgnhYWA9imTRfa2LhQ\nLv+GwAoKgjvnz/fLxXdCXKGhoVSr7VOqV4w9oNVq23RDVFy4QJYubaway0l6vZ6tW3ehVluVlpbd\nKQgO3L9/f7pyu3aRderk7LELk3HjyB49gujk5EoLCy2bNeuQqWFK+vYdQrW6BYF9lMtn0s6uRIYT\n3YglT5O+Xq+nm5sb7927R51ORy8vL964cSNNmSNHjrDDP5nrTYFIST+dFi2MQ76SZOvW3QmsT5XM\nD7J69ffSbTNy5DgqFBNSlVvLunWbm67kT548SUvL6qmqa5IpCKVe2yFl2TLSy+s2VSpLKhRmbN68\nE319fWlmNjzVMS6wWDHX3HobRBcYGEhr60ZpqsksLSvw2rVracoNH05On547MSQnJ/PAgQNcv379\na7+g9XrjPAuXL5MHDhxgu3a92KFDbx45ciR3gipAdDrjzGN//5217fR6fcp4PK9SVZF25e+//547\ngb6DrObObDXZPHv2LNzd3VG2bFkAQK9eveDv74+KFSv+92Fxdg5TJD16BJw7B/j7G5ebNKmNP/9c\nibi4TgDMoFItR8OGtdJtN378GKxb1wDR0a9gMFhDpfoNc+duN7VGqFGjBhwdk5GQMAFJSR1gYbEW\n5cuXgaurK44fP46///4blSpVQoMGxpYnXbsC48d74OnTVxCEZCiVSnz77QwYDEKqo2qQnKzP5XdE\nPB4eHtDpbgH4C0BlAKeRnPwMpUuXNpWJiTFOcn7tWu7EIJfL0bx58wzXPXv2DHv37oVCoUCfPt0w\nefIzHDzYF/HxMwAQBw/2QN++nWFmJqBZs0bo1q1b7gSZj+3dC7i7A56eWd/W+NlJSrWsE30y9GzJ\nzjfMli1bOHjwYNPymjVrOHLkyDRlAgMDaWdnx2rVqrFNmzb866+/MtxXNkMpdBYsSNsrNikpiV26\n9KW5uSUtLGzYrFm713a9DwsL43ffzeSUKb68evVquvVPnjxh9+4DWLlyQw4YMJyRkZEcP/4bajTl\nKAgDKAil6es701S+fXty9ep/t7958yY1GgcCvxI4REGozwkTvsmxc8+P1q5dT5XKhlZWlanR2PN/\n/0tbcf/rr2THjnkf1507d2hnV4IaTTdqtR3p4NCISuUrGod3Jo0Ds7lTLu9EYDYFoSKnTMm4irUw\n696d/OWXd9t2xIhxFIT6BDZQqfyCzs7lsjRBUW7Lau7MVo/cbdu2ISAgAMuXLwcArF27FmfOnMHC\nhQtNZaKjo6FQKCAIAvbu3YsxY8bg9u3b6fYlk8kwdepU07K3t3emOhIVVu+/D4waBXzwQdrXX7x4\ngeTkZDg6OmapLTFJ3L17FwkJCShfvnyaNuF3795FlSr1ER9/E4A9gCewsKiIe/duwMXFBRs2AKtX\nG6+W/nH27FmMHz8dkZGv0LNnB0yc+AXk8sLd7SMiIgJ//fUXTp8+DZJo164dKleuDACoVw+YOhVo\n2zZvY+rUqQ927aoKg2EiAECpHA+5vCt0uiQATQBsB/AjgJMAZAAeQ6l0RUJCTMG+Ws2C2FigeHHg\n7l3A3j7r2xsMBixYsAh79/6J0qWdMX36JLi4uOR8oJkUGBiIwMBA0/K0adOyVpuSnW+YU6dOsVWr\nf59+z5w5M8OHuamVLVuWL168SPd6NkPJ944ePUp39xq0sSnOjh17v/FK4cUL0tKSzKkxtJKSktih\nQ0+q1c7Uat3o6VkjTbPDkydP0tq6zn/qrCvz0qVLfPz4MQ8dOk0rq2Tmo2dXonj+/DldXNyoUvWi\nUjmGguDAwMBAXrlCliqV8w9wM6NWLR8C+1L97jawVKmZlMt30zga66cEWqdar6NCYV4gpgHMKZs2\nka3e3kinwMpq7szWpVnt2rURFBSEkJAQ6HQ6bNq0CR07dkxT5unTp6ZvobNnz4Ik7OzssnPYAic4\nOBht23bFnTtT8PLlKQQECOjatf9ry+/eDfj4AILw2iJZ4ue3GIcOPUd8/D3ExATh3r33MWTIZ6b1\nFStWBBkKYCcAAtgCpTISFy9egqtrZXTpMgqxsX9g/PhzORNQAbVw4SKEh/sgIWED9PqfERe3BCNH\nTsLq1UC/foAYF86tWjWFWj0bwCsA4RCE+fjkEzuoVC3QoMEO1K8fBLX6LIBVAG7AwmIImjZtmeUx\nfgqyzZuBHj3EjiIfye63zJ49e+jp6Uk3NzfOnGmsB166dCmXLl1KkvTz82PlypXp5eXFBg0a8NSp\nUxnuJwdCybeWL19OQRiQ6morgXK52Wt7YHbpQs6bF8GffvqJc+fOZUhISLaO36/f0P8047zIMmWq\npilz8uRJFitWlnK5ki4ubty/fz/ValsC11O2CaFcfoJPnz7NViwF2SefjCEwO9X7eIXFi1emi4tx\njmEx6HQ69us3hAqFOZVKC44YMY7Jycns2vXfNvsXL15krVredHHxZM+eH/PVq1fiBPuO9Ho9J03y\nZYkSFenmVoObN2fcRyIj0dGklZXx7rmwymruzDeZtjAn/U2bNlGrfS9VM8kgqlSWGXaIiosjtVo9\nLS0r0sJiMM3Nh9HSshivX7/+zsefPXsu1eo2ps49SuVktmnTLcOyCQkJJMlz587Ryqp6miof4BX3\n7Ln4znEUdHv37qUglKZx6sowqtVt2L79UtbOBx2U9Xp9mp6lf/xBenuLGFAOmjLl25QHqRcJHKBa\n7cJDhw5latsNG8jWrdO/vmzZclaoUI+VKzfk2rXvPrdBfiAl/XwoISGBVavWp1rdkcBUCkKZ13Zm\n2rmTLFbsJuXy6aZkK5P9xPbte77z8RMTE+nj054aTVlaWlZjmTIV+fDhwzduEx4eTkGwI3ApJY7L\nVCg284cfot45jsJg2bLltLcvTa3WgQMGDGfv3nrOny92VOklJJB2dmRoqNiRZF+5cl4EzqS6+JjD\nIUNGvn1Dkp07k7/9lva1lSt/pyB4EDhEIICCUDrfT37+JlLSz6fi4uK4cOFCTpr0TYa9Kf8xcCDp\n6bmCwMZUf+S7WK9ey2wdPzk5mVeuXOGZM2cy/RBv06YtVKttaWVVlWq1LceNO8H3389WGIVKdLRx\nmIz8WuM1eLBxQpyCrkqVhgT8TZ8HheILfv75l2/d7p+qnf+OL1i/fisCO1J9vlaxbdt3v6gSm5T0\nCzC9nnR0JGfM2EBBqEbgbwLBFIQ6nD17nigxvXjxghcvXuSLFy8YG2v8EGWi53qRsHo12a6d2FG8\n3oEDZN26YkeRfXv27KEgFCMwgwrFZ7SxccnUc65t24y92v/Lx6cTgZWpkv48dus2IOcDzyNZzZ2F\nu2F1AbNs2TWYmT1FyZKJ+PzzbrC2fg9WVg0xcmQrjBs3WpSY7OzsUKNGDdjZ2UEQgJYt/+0lnBG9\nXo9Ro76ArW0JFCvmimXLluddsHlszRqg/+sbYYnuvfeA4GAgNFTsSLKnTZs2OHhwB8aMeYmvvrLE\n1atnUKZMmbdut3Mn8J/GhACAqVPHQa0eD2P/hRnQaL7DxInifL5EkUtfPlmWj0LJUwaDgbNnz6O1\ntQsBP8pke6jRvMdGjVq+tnWPWEJDQ/nJJ4GsUePRa6uIJkyYTEHwJnCXwHkKQlnu3LkzjyPNfWFh\npK2t8cF7fjZwIDlPnJtEUen1pIMD+bobgjNnznDw4BEcNmw0r1y5krfB5bCs5s58k2mLYtJPSkri\n4MFDqVS6EdAQSEy53dRTq61Df39/sUM0OXfuHLVaRwrCxwRi6OnpneGY/m5uNWkc1vmfW+eF7N9/\nmAgR567Zs8lBg8SOIr1jx47Rw6MmbWyKs0OHXty8OZqNGokdVd47fpysVk3sKPJGVnOnVL0jEr1e\nDx+fDvjtt73Q62cA8ARglrJWAdITERERIkaY1pAh4xATMxdxcb8BEHD3blcsWrQ4XTkbG2sA/06p\nqFAEw8HBJu8CzSObNgG9exMBAQGYP38+Dhw4IHZIuHfvHlq37oygoG/w8uUp7NtniYUL++LGDSAs\nTOzo8tbOndKcwa8jJf1c8PDhQ3z88Sdo2bIbFi5cnOG4GHv37sWlS+EwGBoDeAJgBIBjACIBBMBg\nCHjjJNl57cmTJwBqpyzJoNe3woMHT9KV+/nn6RCE0VAovoC5+UDY2m7D558XrvrSu3eN9eTbtn2J\nbt3G4ssvg9C58wh88cXXosZ15MgRAG0AdAZQGjqdH06c2IO2bQ3Yvl3U0PLMuXPnMGbMF/j116eo\nWfMhSMLX9zs4O3ugZMmKWLx4mdghii9X7jfeQT4KJVueP39OR8fSVCgmEthAjaYOx437Kl25VatW\nUaP5kMAVAg4E7hPoS0BJwIIKhQVdXau+dpz7vNar10BaWPQjkEDgIYEorluXcV399evXOWPGd5wz\nZ84bpxYsqGbNIvv0eUm1uhiByJRqrHCqVHZ88OCBaHEZJ8hpmqoTYDAtLLTcscNQaDpqvcnhw4cp\nCI4E/Ai8olbrxAkTJlEQaqZ8zs5QENy4adNmsUPNUVnNnfkm0xaWpP/rr79SELqnqtN+RHNzTbre\nt0FBQRQEBwIHCFwlEEl7+9JUqRxSeh4aKJP9zHLlqoh0JmlFRUWxefNOlMvNaGamprt7MDcXrs9O\nptWoQS5a9BetrGql6bFsZVWFly5dEi2uhIQEVqvWgGp1h5ROgGX5008LGB9v7E9QCL9/06hXrwVT\nTzQkk02lnZ0b0w5It5KdOn0odqg5Kqu5U6reyWHJyckgzVK9YgbSkK6cu7s7tm9fB2fn4VAofoej\n41lMn/4lzMzeB1ADgAzkaDx4cBdRUVF5Ff5rWVpa4sCBHYiPj0FCQgzGj3ctMlUGqQUFAY8fA717\nl4RC8RjAegAJAFbBzOwVPN9llo4cYmFhgdOnD2H27FaYOFGP7duXYezYUVCpgDZtgB07RAstT8TG\nxgFwMi2TzlAo5AAemF6Ty0Nhba3N++Dyk1z68smyfBRKtjx69Chl/tgfUrp4e3Pw4Dd3GW/WjNyx\nw3h7qtFUIBBnGtBLpbJicnJyHkX/drdu3WLVqg1obu5KufwVz5+/9vaNCqgzZ86wXbuebNasE9eu\nXU+S/O478p95gi5evMiyZatQLlfSzc0rwwlr8lpsbGyGYzpt3Uo2by5CQHlo9ux5VKvr0zj/8xEK\nQknOnTuXguBAmewrKhRjaGVVjLdv3xY71ByV1dyZbzJtYUn6JPn333+zQ4derF37ffr6fpdhe/vj\nx49zzpw5XLZsK62sDIyLM7bZ79HjI2q1FanV9qZa7cj16zeKcAYZi4+Pp7OzK2WyhQQiCDyhVtuX\nUVGFbzyeS5cupVS/LSawiYLgxuXLV7BaNfLPP9OWzSjJ5rXbt2/Tza0aFQpzajR2/OOP7WnWx8QY\n52jIRxM+5TiDwcB+/bbSwuIM3d1rmgZSu379Or/+ejJ9fae9dn7hgiyruTNbM2flJJlMVmTm0l20\naCkmTPgOen1XAPawtm6Ox4/rQqFQgCSOHDmCsLAw1K5dO918w2K6du0aGjXqgejom6bXzMy2IzDQ\nCQ0bNkRMTAzWrFmDyMhItGzZErVr137D3vK3Tz/9DEuWOAD4JuWVIyhTZhGSkrbiwQMgP00SRhKu\nrlVx//5QkKMAnIda3RZXr56Cu7u7qVz79sCHHwK9e4sXa24bNQooWRL48kuxI8k7Wc2d2ZoYXZJ1\nycnJGDfuc+h0VwG4ATAgKmoqDh6MQqtWrSCTyeDj4yN2mBmytbWFTvcUxmaltgBikZTUGNbWLxAT\nE4OaNRvj4cNy0Ok88N137bFmzWJ06dJF5KjfTUZTUcbENMeHH+avhA8AL1++xKNHoSD/aRpbB0ql\nN86fP58m6XfqZBxCozAn/YAAYMsWsaPI3/LZn2/hFx8fD4OBAFxTXpFDqXyE8PBwMcPKlJIlS2LI\nkEHQaBpDoRgPjaYxbG0TEBFRAatXr8bDh66Ij9+O5OQfERe3BSNGFNzLraFDP4IgzAewGMBmCMJg\nWFj0zJczMFlaWqZ8Ef2V8ko8DIZr6eZx7dAB2LcP0OnyOsK8ERwMxMQAXl5iR5K/SUk/j2m1WlSs\n6AWFYjKAOAARIHeiUaNGYoeWKQsW/IgNG77Ht9/aYcWKr1C27GW8//4SfPHFJCQkuKYq6YGYmJei\nxZldXl5eOHJkN9q3P4ZmzdZjypQFkMls0aCB2JGlp1QqsWzZYqjVPtBo+kKjqYX27RuiadOmaco5\nOwPlywNHj4oUaC7btw9o1QrI4CZNkopUpy+CR48eoWvXAThzph8sLe9j27YGaN68udhhZdno0RPw\nyy9RSEz0A7ARxl7FuwB4wMJiLNq3N8PWravFDTKH+PoCUVHATz+JHcnrXb9+HRcuXEDJkiXh4+OD\nly9fYsCAT3HixAk4Oblg5coFOHy4Hh49AhYuFDvanNexI9CnD9Crl9iR5K2s5k4p6YtErwdcXIDz\n54FMjBKbL5UpUxWhoath7FcAAB9Brd4LuTwZrVu3xapVi6HVFvw20SRQuTLw229A/fpiR5N5jRq1\nxPnzbtDpJgA4A612NHbsuIqPP3bG/fuF64o4MREoVsw4RIa9vdjR5K2s5s5sV+8EBASgQoUK8PDw\nwA8//JBhmdGjR8PDwwNeXl64dOlSdg9ZIJDEtGkz4ezsDhcXT0yb9i3i4uJM60+eBEqVKrgJHwBs\nbGwABJmWlUoBY8cOQ0xMOLZuXV0oEj4AXL8OxMYC9er9+9r58+cxffq3mD9/Pl6+zH/VWHFxcThz\n5k/odH4AygHoBcAbjx8fgrk5cPmyyAFmQXJycprPTkZOnAAqVCh6Cf+dZKd9qF6vp5ubG+/du0ed\nTkcvLy/euHEjTZndu3ezTZs2JMnTp0+zXr16Ge4rm6HkO3Pnzqcg1CCwiYALATsqlRquWLGKJDl2\nLDltmshBZtPRo0cpCA5UKOZRJguls3M5Ps2vcwe+xZYtW1mhQl2WK+fF7777MU3b+2++IT///N+y\n/v7+VKuLUS7/kipVL5YqVZ6R+awBfFJSEpVKFYEHKR39kqnV1qe/vz/HjSN9fcWOMHNmz55HMzM1\nFQoL1q3bjM9fM23b+PHklCl5HFw+kdXcma1Me/LkSbZq1cq0PGvWLM6aNStNmWHDhnHjxn87GJUv\nXz7DQbgKW9KvVcuHwB4CZQlsSPng3aK5uQ3fe689BeEpf/vtvNhhZttff/3FmTO/p5VVNM+ciXj7\nBvnQgQMHqFa7EAggcIqCUJ0//DCXJGkwkJ6e5Jkz/5YvXboygYOm8VwsLD7knDlzRIr+9WbM+IGC\n4E7gW6rV7VmjRmMmJiYyMNA4flB+t3//fgpCWQIhBPQ0MxvNFi06Z1i2WjXy5Mk8DjCfyGruzFb1\nTlhYGEqVKmVaLlmyJML+M3B3RmUePnyYncMWCNbWlgBuAngJ4601AIRAp5Ph6NGPERenwqeftsGf\nf/4pXpA5oFKlSpg48Uv06aNFYKCt2OG8k9WrtyA+/isArQDUR1zcfKxcuRkAcPWqsYljnTr/lo+O\nfoV/m9wCOp0rIiNf5WnMmfH11xOwefPPGD8+Fj/80BInTx6Aubk5GjUyDg394MHb9yGmEydOIj7+\nQwBlACiQlPQlTp8+ka7co0fGc/nnd/Tq1St8+OEQuLrWQPPmH+Du3bvptinKstU5K6MOLBnhfx4y\nvG47X19f08/e3t7w9vZ+19BE9/33X8Pbuw3i4pIAnAVQF8B8AAsBGDssJSTMwJw5S9M1rSuIunQB\npkwBJkwQO5Kss7QUIJM9x79/ps8hCGoAwObNQPfuaR96dujQDps3j0VCwkIAIVCplqNt2215HXam\ntGvXDu3atUvzmlIJtG1rnGhkxAiRAsuE4sVdoFZvQ1ycAcbHj2dQrFjxdOX27QNatDCeF0m0atUF\nly6VhU63HPfvH0b9+j4ICroCa2vrPD+H3BAYGIjAwMB330F2bitOnTqVpnpn5syZ/P7779OUGTZs\nGDds2GBaLirVOyR548YNdu/ek2Zm1rS0bE653IHAxlTDvK5g27Y9xQ4zR+h0xjljHz4UO5Ksu337\nNi0ti1Em+5LALApCMQYEBNBgIN3dyfP/qYWLi4tjv35DaWXlzOLFPQvk+Oxbt5ItWogdxZslJCSw\nbt1m1GrrUqvtQY3GgceOHUtXrkcPcsUK489PnjyhhYVtyqBr/wx53Yx79uzJ4+jzTlZzZ7YybVJS\nEl1dXXnv3j0mJia+9UHuqVOnisyD3NRCQ0O5e/duzps3jypVfQLxBDZQrXZmQECA2OHlmL59yUWL\nxI7i3dy5c4fjxk3gp59+xpMplcMXL5KursZ6/cImOprUasmXL40Dla1Zs5Z9+gzmhAmTGB4eLnZ4\nJjqdjjt37uSaNWt4//79dOuTktJebERGRtLMTEPgVaoH2DV46NChPI487+Rp0ifJPXv20NPTk25u\nbpw5cyZJcunSpVy6dKmpzIgRI+jm5sZq1arxwoULGQdSiJN+agMHXmGxYvvYtGl77t69W+xwctQf\nfxSu4Xu/+sr4r7Bq04bcuJGcMuVbCkJlAotpbj6UpUqV56tXr8QOL0OhoaE8cOAA79y5Q9L48LZq\n1bRlPvpoOAWhAYHFVKl60MurIXU6nQjR5o2s5k6pc1Yea9YMGDeucE7aHBdn7HB27x5gZyd2NNlD\nAu7uxsG7atYUO5rcsWwZ8OefxLZtVkhMvAHA2OBCo2mPJUt6ol+/fuIG+B8bNmzCoEEjYGZWBQkJ\nl9G9eyc4Oi6AmZk1fvzx33IGgwHLli3HiRMX4OlZBp9//hk0Go14gecyqUduPvbiBeDqCjx5AqjV\nYkeTOzp3Nv7r31/sSLJOr9dj6tTvsH17ACws6iA8/EeEhqoKVc/Vly9f4qOPRuDPP/+EnV0VPHu2\nE3FxtkhOfgzAEgAgCP0xf35TDB48WNxgU4mKioKzcxnExx+GcbjrMADFIJfPxNy5Fvjss6oiRyie\nPO+RK8m8//0PaN688CZ8wJjwC+o0iqNHT8DPPx/BzZs/4vLlwXj6dCkuX76E9u17wsJCAzu7Eli9\neq3YYWZL5859sXevgMjIYwgO/gixsddQs+Z4qFR9YWxl9gsUin1o1aqV2KGm8fjxYygU9gCuAYgF\ncB7AfhgMXpg3rwBeYYhIutLPQx07Aj17GieyKKwiIoBy5YxtpwvaHbWlpSNiYi7in2oOpXIWKlTY\ngaCg8khMXAAgGGp1Bxw4sKXAjIqaWlJSElQqDQyGGAA7AAwBMBbm5qXRtetxnD17GU5OxbB48Q/w\nymfjE8fFxcHZuSyiozsAcADwz5AvOqjVToiLixQxOnFJV/r5VHQ0EBgI/KfJdKFjZwfUrWtsO13Q\nKBRmAKJTLd9EUNBtJCZ+D8AGQC0kJn6EQ4cOixVitiiVSiiV5gCOARiZ8r8vdLruOHbsJIKCLuDE\niYB8l/ABQBAE7NixEWr1NgCrAIQCIOTyPahVqwCNgpcPSEk/j+zdCzRqBNjYiB1J7isoVTwRERE4\nfPgwrly5ApL45psJEITOAK5AJjsIS8tA2Ns7AbiRsgVhYXEDDg4Fc1QvmUyG776bAXPz3gAaAKiW\nssYST57Y4dWr/NerODUfHx+8ePEYEyYMhlJZAcATeHisw5YtK8UOrUCRqnfySK9ewPvvA0OGiB1J\n7nv0CKhSxfjA2txc7Ggydu7cObRo0RGAB5KS7qNz55ZYs+YXbNy4GYMHvw8vr6lo3FgDQRAwe/Zi\n6PU9oVQGo1Spp7hw4c8C3Rpkzpw5mDTJD0lJfwHQAHgGpfJXJCR8CYVCIXZ4mXLhQhK6d5fj7t2C\nEW9uklrv5EMJCcZZi27fNo75XRQ0aABMmwa0bCl2JBkrV64qQkK+AdATQBy02kZYs2YqXFw6oXnz\nxzAYOiMhwQdqtT+6dm2E6tUrwdraGr169YIgCGKHny0k8fHHn2Lr1kOQy72g0yWhePGVuHu34Iyd\n9PPRxAsAACAASURBVOOPxvGD/PyMyzqdDub59Qojl0lJPx/atQuYPbvwTlOXkR9/NLbXX7JE7Egy\nZm4uICnpKf5ppmhuPhbffVcCV6/2w8aNm5CUNBSACsALmJu7IiwsGA4ODmKGnKNI4vjx4wgLC0O1\najXRtKknLl0yzvFQEPj4AGPHAm5uN9CuXQ/cv38LtrbO2Lp1DZo1ayZ2eHlKepCbD23fbhyQrCjp\n3Bnw9wcMBrEjyVj58l6Qyf6pC34GM7NdqFbNC/v2WcPC4iKMCR8A7GFmZpvv67uzSiaToUmTJujV\nqxcqVfI0DcCW2qlTpzBz5kwsX74cCQkJ4gSagZgY4Nw5oEkTPXx82iMk5DOQOkRErELHjj3x5MkT\nsUPM16Skn8v0euOH6YMPxI4kb3l4GGcxOno0IV/ewf3xx2q4uCyEVusKc3MPjBnTF1ZWLWBtbQaF\nYj+A1QDCIZf/CHt7NcoU5CnOMqFTJ+OX9D9Wr16L5s27YsqUl/jss+2oV88n3yT+I0eMLcRevnyI\n6OgkAIMByABYwmAokb0RKIuCdx/xIWflo1By1OHDZK1aYkeR9y5fvkxLy4WUyebS2tqJBw4cEDuk\ndHQ6HW/fvm2ajWn0aHLqVGPs5cvXolptw9q1vXn37l1xA80D0dGkpaVxADaStLJy4v/bu/P4mK7+\nD+CfyewzWSyJNBIRgiS2WFKKhLQMsQu1FUUpTy3VFk9VFX1asRRtVX+liiqtrWLpg6A0WmseaxFb\nERUituwz2WY+vz8mImkSTLbJct6vV141d86993unk29mzj3ne4BTWUXLTNRqO3Lt2rXWDTLLuHHk\n/PlkQkICFQpbAjcIDCXgSaA1NRpHHj161NphlhpLc2eZybQVNemPG0fOmWPtKEpXWloanZzcCfxC\nwETgN2q1joyJibF2aAXKyCCdnckrV6wdifV060auX2+uuimTKQkkZ5cnVqn+xSVLllg7RJKkpyd5\n9qz534sXL6FCUY1A46zqtSTwM93dG1o3yFJkae4U3TslKDMT+Pln8yzcyiQ6Ohrmdax7wPy1OxAy\nWVP8+eef1g3sKfbvNy9SX7++tSOxnsddPBKJBIGBQVAo3gFwH8ABSCQ/l4kbpH/9ZS7s16SJuVZS\n586vYODA7pBKX8GT+zA6xMTcsGaYZZpI+iXowAFzIvH0tHYkpcvR0RGZmXEAorK2pCIj4zJcXFys\nFlNmZiaioqIKvCG7bl3FLo/xPHr2BMLCzMtDbt78PTp2jIdG44WaNf+FzZu/R+PGja0dIsLCgKAg\n4MGD+2jcuDVeeqk3Nm7cCWALgBgAgI3NMjRq1NKqcZZpJfSNw2JlKBSLHDhwgF5efnR09OCQIW8y\nOTk5+7mRI8nFi60YnBV9+eXX1GhqUqX6D21sIjlhwhSrxXLlyhW6utanRuNKhcKWc+YsyPV8cjLp\n4EDms6BbpdO6Nbl3r7WjKFiPHuY1AIKDh1Iufzer+zCVMpk3pVI11eoXWLt2w0pxH+YxS3Nnmcm0\n5THpX7x4kRqNI4GtBK5QpRrA4OAhJMnU1PK7fGBxOXXqFL/55lva2cVz6tRVBS6gU9J8fF6kRLIk\nq783mhpNbf7+++/Zz//4IxkUZJXQypyQEHLCBGtHkT+93nyz+dEjsm7d5gQiciw9uox9+w7l33//\nzczMTGuHWqoszZ2ie6cI9u7dC6OxP4A+AOojNXUZdu7cBsD8NbRpU8DV1aohWpW3tze+/nolDIZ9\nWLSoJvz9u2LLllCcP38eOl0wmjYNwIwZ/0FmZmaJxUASly+fAjkma4srjMbuOH36dHabH38Ehg4t\nsRDKld69gW3byub8igMHzAvaVK0KNGrkBZlsKwACyIBa/QtefLEpatWqVW5KSViLzNoBlGe2traQ\nSqNzbImGSmULANiwwVxvpzL76aefcP16VWRm9gMggcEQijFjBiEjIx3JyTNANsa1a58gNvY+Vqz4\nqkRikEgkcHaug5iYvQB6AtBDJjuEOnWCAAD37gGHDwMbN5bI6csdHx/A1haIiABeKmPFK//7X6BH\nD/O/ly9fjLZtdXj48L8wmZLh5+eDd99927oBlhcl84XDcmUolOeWlJTEunUbU6kcTOBTajTu/Oab\nb7P7iLOGf1daCxYsyOp3ffwVPIEymZIq1cgc22KpVNqVaBx//PEHbW2d6ODQiVqtB197bRRNWaud\nf/UVOWRIiZ6+3PnoI/K996wdRW4mE+nmRl68+GRbamoqIyIiePbsWRqNRusFZ2WW5s5C19559OgR\nBg4ciJs3b8LDwwObNm1ClXzqBnt4eMDe3h5SqRRyuRwRERH5Hq+81t5JTEzE8uXLcenSFZhMRjRs\n6ANb21HYsaMadu+2dnTWdeLECXTo0AN6/VYAzWBjcwQ+Pv/GjRsNoNf/CGAugFUAHmL58oUYM6bk\nlue7d+8eTp06BScnJ7Ro0QKSrDUQW7cGZs8GunYtsVOXO+fOmT9RR0WhzCwVeeYM0L+/uWhhWYmp\nrLA4dxb2r8vUqVM5f/58kuS8efP4/vvv59vOw8ODDx8+fObxihCK1R0/fpxarSOl0ncpl4+hTBbG\nhQvvWTusMmHTps10dHSnQtGECkU8L178i05O7pRIXiHQlMAZAkeo0dThzz9veeqxQkND+c47U7h4\n8WKmpKQUObZz50hXV/PELOEJk4n08iKPH7d2JE/85z/kO+9YO4qyydLcWehM6+XlxbtZY9xiYmLo\n5eWVbzsPDw8+ePDg2YGU46Tfvn13At/l6LLQc/hw6w1RLKteeonctYuMjo5mtWqeBPbleM2+Y3Dw\nsAL3nTXrU2o0XgTmUqXqQ1/ftkxLSytSPO+8Q374YZEOUWHNmEFOKeW38MqVq1m1qiuVSjsGBw/J\nNfy5VSty//7Sjae8sDR3Fnr0TmxsLJydnQEAzs7OiI2NLfCrR6dOneDn54cVK1YU9nRlWlxcAoC6\nWY8uATiCc+eOlOiolPLo9deB1asBV1dXNGrkBeDJTXAbm2hUqWKb736ZmZmYM+dT6PW/AZiG1NRQ\nXLtGhIWFFTqWtDTzhKw33ij0ISockti9ezeWL1+Ohg0jsXmz+c9xaQgPD8fEiTMQF/cL0tJuYPfu\nTIwebb4xGxtr7tbx9y+dWCq6p47e0el0+ZYpnTNnTq7HEokku4/0nw4fPgwXFxfcv38fOp0O3t7e\nCAgIyLft7Nmzs/8dGBiIwMDAZ4RfNvTv3x3Xrk2HXt8GwEQAl3HhAtG1az/s2bMVNjZiZCwADB4M\nfPAB8OABMG/eh9DpesNguAobGz202vX44IM/8t0vPT09q8/SKWuLBEBNJCcnFzqW7dvNQ2rr1n12\n28qAJAYNegO7dp2E0dgMmZnToFZfxJ49cgQFlfzykHv3/gq9fjSA5gCA1NS52LOnPQDgl1/Mi/FU\n0jVS8ggPDy9aJdHCfqXw8vLKLqB1586dArt3cpo9ezYXLlyY73NFCMXqMjMzOWnSVAIdCaRndVek\n09a2IQ8ePGjt8EpcfHw8R4x4i40bt2P//sOzu/3yM2zYk1nKf/75Jz/4YAZnzpzNGzduPPUc/v5d\nqFC8SeAygR9oZ1eDt2/ftijOkydP0senFe3tnVm16kkuXfrIov0rsj/++INabYOsipWeBLoT2ECl\n8mteKYUqdIsWLaJSOSBHd99O1q3rS5Ls0oXcuLHEQyi3LM2dRbqRO2/ePJLk3Llz872Rm5KSwsTE\nRJJkcnIy27Ztyz179uQfSDlO+iR59+5d2thsypoWbn7j2tt35fbt260dWokyGo1s2bI9lcpRBMIp\nl09hnTqNaDAY8m0fHk42amS+WWiJuLg4BgcPpZNTHTZt2o4nTpywaP979+7RweEFAj8QiCGQTC+v\nttlDNyu7n3/+mfb2vQm8k/XzOPnGMSiof4mfPyEhgZ6eTajR9KRCMYEajSP37NnDR49Ie3tz6Wch\nf6WW9B8+fMiOHTuyfv361Ol0jIuLI0nevn2b3bp1I0leu3aNvr6+9PX1ZaNGjRgSElJsgZc19++b\naGOTSBubTwncJbCBdnY1nvqptyK4du0aNRpXAsbs2ut2ds15+PDhPG2Tk5NpMKSyXj3S0nLniYmJ\nTCrCb/6OHTtob98lRzIzUaWqzujoaK5Zs4YzZ87ijh07Cn388i4qKiqrpIiOwNocr1MS7e17sn37\nnpwx4+Mi3zx/mqSkJK5YsYKLFi3iuXPnSJLff0/26VNip6wQSi3pF7fynvQ//5zs2zeF/v5B1Gqr\ns3795oyIiLB2WCXu5s2bVKtrEEjNShJG2tr68HiO8X4pKSkMCupLmUxFqVTJl176haNGPd8n7NTU\nVPbuPZgymZoymZoDB45gRiHGWB48eJC2tg0JZGTF+YAymZo6XW9qtf6USGZQq/Xh1KkzLD52RREW\nFka1uiqBhgTuEYglMJ/AfgKhVKu7s2fPgaUaU8+eZBlZu6XMEknfCkwmsmFDshJ03+dhMpkYFNSX\nanVXAj9QpRrEFi0CciXmMWPepko1IOsPwyOq1V2pVqcy68vhU02bNpNqdXcCegLJ1Gh0/Pjjgr8x\nFsRoNPLll3tQoVhA4BK1Wm8OHz6KWm19AmlZfwjuU6Gw5aNHlbev32QyceLEKZTJVLSxkVEq7Zmj\ny9JAhcL+uYZgF4eEhNyreQn5szR3imElxeDIEcBoBAoYlFShSSQSbN++HtOnt0ePHrvx7rsN8Pvv\nuyGTPRkYFh5+FKmp7wBQAqgKg6EvnJxOYeXKpx/baDRiy5ZdMBjGAVAD0EKvH4vw8OMWx2ljY4M9\ne7aiRo1RGDLkGNavX4BBg16FTFYLwONhIdUhk9khKSnJ4uNXFBKJBEuWfIa0tBT89787oNE8hHm0\nFLL/y1Iax7lzp/l3ysGhVE5XaYiCa8VgxQpg9OjKOz1coVBgxoxpBT7v7u6Kv/46ApOpDQBCoTiK\nDh0ysGRJG0yaBMjyeRcajUbodH1w/fpdAAcBdAMAyOWHULeuW6HiPHxYBju7ali7djgkEuDhw4eQ\nSC7CvAh6Z0ily+Hi4gTXylwaNYuNjQ06dOiAatUmIyVlM0ymdlCrx6N9+45wdHQslRg2bTIiIOAB\nUlJsodVqS+WclULJfOGwXBkKJY9Hjx7lmh2YU1wcWaUKeU9UXSjQlStXWK2aK+3setDOrgPr1fNl\nXFwc27UjN23Kf59t27bR1vZFAjezhhC+TMCP7u7evFfIF7tPH/L//i/3ttOnT9PHpxVtbR3Ztm1n\n3rp1q1DHrqhiY2M5cOC7lEqTOWHCJwWOynpe6enp/OKLLzly5FtcsuSrAu/PbN16gEACNRpfajRV\nuWVLaJHOW5FZmjvLTKYti0k/ISGB7dp1pkJhR5lMzbFjJ+UZ4rd0KTlggJUCLEfu37/PTZs2cdu2\nbdl1c37+mWzbNv/23377LTWax9U4EwiEUiKxKXR/+4ULZI0a5lWyBMu9+ir57bdFO4bJZGKXLsHU\naHQEllCjeYU9egzI8zuVmJhIpfLtrJvJJHCCGk317HlBQm4i6RejIUPepFI5MmvERxw1mhf53Xcr\ns59PTU2jj08qf/lFb8Uoy6/MTNLDgzx2LPf2pKQkBgcPpkRiR+AogTRKpdPZvHlAgce6cuUKf/vt\ntwK/BQwdSs6ZU5zRVy47dpBt2uTdHh8fz65dX6VCoWW1am786af1BR7j/Pnz1Gjcc9w4N1Ctdskz\n+evPP/+kVHosx7BR0sGhbaWY6FgYIukXIw+PpgRO5njzfc1hw8aQJI8cOUJb2yBKJFFUKqvwxx8L\nfrMLBfvyS7JXr9zbOnbsRZVqcNZwwWoEbNismX+BM3CnTZtFtboGHRz8qdU68tdff831/LVrZPXq\nYhRIUWRkmOvZnz6de3uPHgOpUIwgEEfgODWaF3jsn3/Fs/zvf/+jnV3jXHMlbG0b8OzZs7nanT0b\nR+AhgYtZ7aKoVldnVFRUSV1euSaSfjEKDOxBiWRx9htUqRzIjz/+lGlpaaxSxYVAVNZzf1KtdqxU\nizEXF72erFmTfDzBNiEhgTKZJkc5C9LWtiu3bMm/7PLx48ezPj3ez2p/gPb2Trm6DEaMMFeNFIrm\nk0/IMWNyb9NoqmaN5zf/v5JKpxQ4CTM1NZW1azekVPoRgTOUyT6gp2dTpqen52oXEkJ26HCFarUj\nHRxeoVrtxC++WFpSl1XuWZo7xeidp/j228Vo0+YVZGTsARkHDw8bTJ68EjExMUhLswNQO6tlE8jl\nLXHhwgXUqVPHmiGXO2o1MG2aeSGTX34B5HI5ABOAZABVARASSSIUBVTbunr1KqTSNgAejyh5GQaD\nHgkJCahSpQrOnwd27TJXaRSKZvRo83KKCxY8GUZpb18dev1FADUAEErlRVSv3ivXfpGRkZgzZzES\nE/WYPv0dhIbuQWRkKJo0aYjvvgvL+n9uZjIB330HrF9fH87OJ3D58mV4enrC09Oz9C60oiuhPz4W\nK0Oh5PLw4UNu27aNYWFh2VPQ9Xo95fK3s77Smpf8U6tf4Pnz560cbflkMJi7Dh5Xbhg7dhI1mlYE\nllOpfJ1eXi0KHDVy5swZajQ5v3VtoaNjrexP+j17PinwJuSVlJTE0NBQbt68ObuUytMMHEguWfLk\n8fbt26lWO1Euf4M2Nh5UKJz52mujso91+fJl2to6USKZS2A1NRoPrly5OtcxTSYTf/zxR06bNp3/\n/vc+Nmtmsrg2U2Vmae4sM5m2rCb9gtSt+5BK5UA6OOioVr/AmTM/tXZI5drataSfH2k0mmfPfvPN\ncg4c+AanT5/JhISEp+77+edfUam0p51dfVap4sL33/+APXoMZs+eX7NWrUymppbSRZQz9+7dY61a\nXrS17Ug7uyDWqOHBv//++6n7HDxIenvnLph37NgxVq3qShub9wn8QYXiTbZoEUCj0cgpU6ZRIpmW\nox8/nHXrNst1zKFD36RW60fgY0qlv7JFizWiEJ4FRNIvBadOke7u5PXrN7lr1y5GRkZaO6Ry7/79\nh3R1vUV//++5efNmi/d/8OABIyMj+fbbU6jRtMgqGhbLKlVGP9cn2MpozJiJWd9YH/fHz+Krr77+\n1H1MJrJxY3Lv3ifbfv/9d9rb++VI7EZqNDV5/fp1vvvuVAKzczx3jO7ujbP3vX79elbtpqTse2cq\nVX1eunSppC67wrE0d4oyDIWwYgUwahRQp447unbtCh8fH2uHVK4lJSXBz88fsbHf49ChV/H664sw\nZ84Ci45RvXp1eHt745tvvoZevxPAUAA1kJFxHzt27CiRuMu769dvIyOjXfZjo7ENbty4/dR9JBJg\nyhRg3rwn2+RyOUwmPcz3YgAgHSZTGhQKBV5//TVoNEsBrAawG1rtaEyY8GS5ssTERMhkjgAer5om\ngUKhQXx8fKmVe6hsRNK3UEoKsGGDWGavOIWGhuLBA09kZs4AoIXB8Cs++WSOxb/0JEGaAGhzbNOI\nZSsL0KlTW2g0/wcgCYABavVSvPJKm2fu99prwF9/AcezSiD5+fnB29sJKtVgAN9Do+kNna4Tatas\niTp16mDZssXw9/8Zfn6LMG/eOEyZ8k72sby8vGBnlw6J5AsARgDLkZZ2G+3atYdWWxULFiwugSuv\n3ETSt9DmzUC7doBb4cq/CPlITU2FyZRzST4VMjJetTjp29jYoG/f0ZBIEgGcBKBDevpeREffgclk\netbulc6UKe+gXz8vSKVOkEqrIijIHp98MuOZ+8nlwNSpQEiI+bFMJsPBg7swZUpD9OmzH9OnvwIP\nDzc4OtZG1aou+Ne/PsHp08fx8cfvYcKEt3ItrapSqXDo0F64uysgl+9E9erzAQTCaHwIg+EUPv74\nG2zfvr2EXoFKqgS6mAqlDIXyVG3akBV8MaxSFxUVRVtbJwKrCZyiQvE2FYoE5ijJ/1wyM8levYxs\n3Pg4FYrqlEiGZY0Y8eeIEf8qmeArAIPBkF0a43np9aSra97Z1KR59JVKFUCgKoGzWX31R6jVVs/3\nprzBQNaqRUZEkDVrehE4n+MewGd8661Jhb20SsHS3Ck+6VsgMhKIigK6dbN2JBVL7dq1ER6+Gy++\nuBa1aw/HiBHAunVK9O1r7kZ4HiQwfjyg19vg008fQqn0ArkGwAjo9Tuxbt33SElJKcnLKLdUKhU0\nGo1F+0RFXcSrr57D22+n4p9fyDZs2ITU1PEAfAA0zdraBjY2NXDz5s08x/r6a6BFC+DFF4EaNWoA\nOJP1DKFQnIWraw0Lr0h4GjE5ywJr1gDDhuVfClgompYtWyIiYn+ubfHxQPv25rrqzZsXvG9qqnni\n0NWrwK+/AgcOpEMiscWTOvAqSCTS7L79K1euYNmy75CWloHXXx+E1q1bl8xFVSDnz5/H559/g7S0\nDCgUEmzYsB1yeTMkJX2OqVMfYuFC/+y2KpUGCQkaAJcAXAPgCeAcMjJi4PaPftH4eGD+fCA83Px4\n2bLP0LFjD5C/QiK5C2fn25gwYWkpXWUlUULfOCxWhkLJV2amuVzAhQvWjqTiefjwIY8ePZrvGPGf\nfzbXzZk7l/zHbH2S5KFDZIsW5kqnj3so4uLi6ORUm1LppwR+p0o1kJ06mQv8XLx4MWuy0HQCIdRo\nnLh///6SvLxy788//6RW60iJ5FMCHxCwp3lxeRK4RuAmY2KelC9duXI1NZpaBF4lYE+JpAnV6mr8\n6acNeY793nvkG2/k3nb9+nUuX76ca9euLbCkufCEpbmz0Jl206ZNbNiwIW1sbHjy5MkC2+3evZte\nXl6sV68e582bV3AgZTzph4WZJw8JhZeUlMTRoyeyYcM27N37Nd66dYu//vortVpHOjj4UaWqxvnz\n806fvX6d7N7d3Ic8bhy5cCE5cybZoYO5L3jNGvOkrpxu3LjBbt0GsGHDNhw7dlJ28njjjXGUSP6T\no8/4J770UudSuPrya+TItyiRhGS9XrsIBOaqgCmTbeSwYbmr2e3Zs4djx77N8ePf5tatW/Mtlnfs\nGOnsLNaiKKpSS/oXL17k5cuXGRgYWGDSz8zMpKenJ2/cuMH09HT6+voWOJGprCf9wYPJr76ydhTl\nl8lkYrt2nalUDiXwO6XSmXRx8aSdnROB37ISyC1qNC/w3Llz+R7j/Hly0SJy0iTyww/NN9QtXdOj\nf/8RBL7JkbR+ZZMm/sVwhRXX4MGjCCzNrniZ+wbtTtrbe9HV1cSwsOc/psFA+viQG/J++BcsZGnu\nLHTvtLe39zPbREREoF69evDw8AAADBo0CNu3by93k5kSEsxFu776ytqRlF+xsbE4ceJ/SEu7B0AG\nozEASUl7kJ4eByAwq5UbZLJWuHLlCho3bpznGI0amX+KYuTIAdi5cwz0ek8AttBo3sUbb4wp2kEr\nuFGjBmPbtqEwGGoCiIJEkgmJ5CWoVI6QyzOwc+fPMBol6N8fOHgQeFZqMJmAkSMBX19gwIBSuQQh\nhxIdvXP79m3UqlUr+7Gbmxtu3376jL+yaPNm4JVXgBs3TsDfvyt8fF7CBx/MQkZGhrVDKzfkcjnI\nTABpWVsIID3rpvivWdv+RkbG8ef6QFFYXbt2xXfffQYvrxmoW3ccZs0agUmTxpfY+SqCjh07YsOG\n5XB3/xASyacg34Zc3hk1amhx40Yk2rVrh/btgblzge7dgWvXCj4WCXz4IfDXX+moWzcEU6a8j0OH\nDpXexQhPH72j0+lw9+7dPNtDQkLQs2fPZx5cYuFK4bNnz87+d2BgIAIDAy3av6SsXw/07RuDwMCu\nSEmZB8ALS5bMRFzcVCxb9oW1wysXqlevjt69g7FzZy/o9a9DqTyA2rXl+PzzDejb9zXY2LggPf1v\nhIR8goYNGxbbeUnizp07MBqNqFWrFiQSCQYPHoTBgwcV2zkqg169emHEiHEg9wFogbQ04t69XggN\nDcWoUaMAmGepp6YC/v7mWesdOuQ+hl4PvPMOcOhQBmJjW2HBgrbIzKyJZcv6Y926/0NwcHDpX1g5\nFB4ejvDHw50Ko6j9SU/r0z969Ci7dOmS/TgkJKTAm7nFEEqJuH+ftLcn5879kgrFuBx9wdHUaqtb\nO7xyJSMjgwsWLGKvXq9x6tTpTExMJGlecu/EiRPFvgZqWloau3V7lSpVdarVznzppY7Z5xQsp1Ta\nZa1oZf4dUCgmctGiRXna7d5tHunWpw+5ahW5ZQs5a5b5RvzQoeT06fMpk43N8bu0L0/lTeH5WZo7\ni6V7hwVMl/fz88PVq1cRFRWF9PR0bNy4Eb169cq3bVn1yy+ATgfY2trAxiYxxzOJkMnyX9hDyJ9M\nJsPUqe9h+/YfsWDBHNjZ2QEAHBwc0LJlS7zwwgvPdRyS0Ov1z2w3f/5i/PZbClJTo2Ew3Mbp066Y\nPPnDIl1DZdalSw8olRMB/A1gD2SyDdDpdHnaBQWZF63p3h3Yv988vyUlBdixA1i7FkhPj0NmZs0c\ne9RESkpyaV2GUNi/LqGhoXRzc6NKpaKzszODgoJIkrdv32a3bt2y2+3atYsNGjSgp6dngcuokWX3\nk3737uRPP5lrjzs5uVMme4/Acmo0DbhggVido7Rt2LCRarUDpVIl69dv9tQlKrt2HUDgxxyfKA+w\nadOCF1cXni4pKYn9+w+ng4MLa9duzN27dxfqOEeOHKFa7UwgjMA5ajQvc9KkfxdztJWHpblTkrWT\n1UkkkjJXSjUx0VxYLToasLcH7ty5g3nzFiM29hGCg7tg0KCB1g6xUomMjISfXyAMhr0AfGFjsxD1\n6m3A5csn820/Zcp0LF0ajbS07wFIIJe/j+Dg+9i4cXVphl1hxcTE4IcffkBqahr69eub74irguzY\nsQOTJ3+MlJRkDBwYjAULPsm1bKLw/CzNnSLpP8XmzcCqVcDu3daORACANWvWYPz4fUhJWZe1hZBK\nVUhKiodarcYXX3yFBQu+gslEjB8/CpMmjYO/fxfcuJECiUSF6tVTcPTo/ufuRhIKduvWLTRrGhms\nGgAADmZJREFU1gZJSd1hNFaBSrUKYWGhCAgIsHZolY6luVNUkXmKvXuBrl2tHYXwmIuLCySSszAP\n+1QCOAOlUgOVSoUffliHDz/8Gnr9egByzJ//OqpUscfJk7/j+PHjMBqNaNWqFdRqtXUvooJYtGgJ\nEhIGw2j8DACg1/vivfdm43//2/+MPQVrE1U2C0Cak37nztaORHhMp9OhU6emsLX1g63tEKjVXTBv\n3ifYvHkzli5dDb1+JoCWAJoiJeVT/PTTDsjlcvj7+6NDhw4i4RejR48SYTR65NhSBwkJiQU1F8oQ\n8Uk/h3XrfsKqVZug1arRt+/bIF+Cl5dlcw2EkiORSBAaug779u1DTEwMUlLaYerUWZBK20OvPw8g\nKkfrv+HgYFvAkYSi6t+/B7ZsmQi9/kUAVaDR/BsDBjx77o5gfaJPH0BaWhomTpyENWv2ID19FIAv\nAAyHVOqL3btd8h2WJlgXSTg4OCMpaTuANjDXYG8HG5vRABRQq7/H77/vQYsWLawbaAW2YsVKzJo1\nH+npaXj99dfw2WefQiqVWjusSkfcyLVQamoq2rTphLNnr4JcB2A4gG8A9AYQCa22A65fv5C1uINQ\nVqSlpUGjsYXJlI7HdfPV6r7o3Jnw9W2GwYMHlmg5B0EoK8SNXAutWrUKly9XBVkTwF0AdjAnfABo\nCJnMCxcvXhRJv4xRKpXw9GyMv/5aAnISzAt2HMF//rMXTZs2fdbuglBpVfobuXfu3IXB0ALAWwBm\nA7gD4HFRuPtIT78KV1dXa4UnPMWuXZvh7v4tFAoHKJUv4uuv54uELwjPUOmTfocOAdBofgDQEcBH\nAOwBfAmpdA+Uysbo0ycI1apVs26QQh5xcXE4ceIEQkI+xMWLp5GcHIeRI4dbOyxBKPMqfZ8+AHzx\nxVJMm/YBMjLSEBCgg1S6GteurcC9eyuhUNSGRHIZv/22C82aNbNKfEJut2/fRsuW/khJaQxAAo3m\nT5w8eSjP+quCUBmIG7mFRBKZmZmQy+VwdEyBXj8CBsM6mCcB/QAfn6WIjIwAAFy6dAlbt26FUqnE\nkCFD4OzsbLW4K5rjx49jxYq1kMmkGD9+NJo0aZKnzbBhY7B+vSOMxhAAgFT6Efr3v4P161eWdrjC\nP6SlpeHAgQMwGAxo3749HB0drR1ShSdu5BaSRCKBXC5HdDRgMAAGQwO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"text": "" } ], "prompt_number": 156 }, { "cell_type": "markdown", "metadata": {}, "source": "Neural nets use sigmoids. Our sigmoid basis will be kind of like a neural net, but we won't modify the basis as we train." }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=sigmoid_basis)\nmodel.fit_normal_eqns(X, y, 0.1)\nXn = arange(-8, 8, 0.05).reshape((-1,1))\nyh = model.predict(Xn)\nscatter(X, y)\nplot(Xn, yh)\ntitle('Sigmoidal basis')\nshow()", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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1mrapb/BdlKSSPHnyZP4HXEyMHPkpNZp2BO4SOEdJKsc//vjDtP7u3bssUaIU5fIpBDZS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\nRCR9QRCEGuT/AYg+A3XCqV5pAAAAAElFTkSuQmCC\n", "text": "" } ], "prompt_number": 155 }, { "cell_type": "markdown", "metadata": {}, "source": "Suppose we know the function is locally linear. We can use heavyside step functions to approximate it." }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=heavyside_basis)\nmodel.fit_normal_eqns(X, y, 0.1)\nXn = arange(-8, 8, 0.05).reshape((-1,1))\nyh = model.predict(Xn)\nscatter(X, y)\nplot(Xn, yh)\ntitle('Heavyside basis')\nshow()", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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b4Af805G4GuDEunU/sHz5Ss6cCebFF7vy9tuDn+t8BoMWtRri4myDhhRP5uFR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\n0qlTJ+bNm5djOY1GQ2RkJNHR0WUq4d/h5eXFo48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O5uGHO3P+vKDRVEanm8De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\n+oqiKOWISvqKoijlyP8Dm/SFWbj3tHYAAAAASUVORK5CYII=\n", "text": "" } ], "prompt_number": 154 }, { "cell_type": "markdown", "metadata": {}, "source": "Interesting. Let's try some different data, making it non-centered so the bias becomes important." }, { "cell_type": "code", "collapsed": false, "input": "X = arange(-10, 10, 0.5)\ny = 0.8*abs(X)**0.3 + 2 + randn(X.shape[0])*0.1\nscatter(X,y)\nX = X.reshape((-1,1))", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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wK7n1rhB15LHHniU7exSFhd9TWLiVrKw7eOqpF7SOJRo5KepCXKeDB49RXh5z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\n37/iPUtOTtY6kl0kJycTFBR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"text": "" } ], "prompt_number": 182 }, { "cell_type": "markdown", "metadata": {}, "source": "Linear basis, no bias" }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel()\nmodel.fit_normal_eqns(X, y, reg=0.1)\nXn = arange(-10, 10, 0.05).reshape((-1,1))\nyh = model.predict(Xn)\nscatter(X, y)\nplot(Xn, yh)\ntitle('Linear basis, no bias')\nshow()", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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gc5g2barB/VpYWODxx5/CwYNTUV09B8AJACl4/PH3ceTIEUyZ8jZu3LiOIUMGY/nyxbCz\ns2vQh0gkQnr6Xsya9QnOnPkv+vbtiaSkmVy/Z83q7ndkw4YNuHHjBiIjd2rq8g8rJiYCv/++CHJ5\nBAALSCQLMWxYdNME3ALIZDLIZLJGz2/Ue9p+8sknEIvFeOedd3S28fHxwR9//NGg9NPWDto2pdLS\nUrz00jTIZAfQvr0rVq5chE6dOqFnz3BUVCQDCIa19RwMHarGrl2bTB0ua6NqamqwePFX+P330+jZ\nsyveeedN2NjYNGsMKpUKU6e+iTVrVgAAJkyYhOXLl8DS0jzOONc3bxqU8IuLi2FpaQknJydUVlYi\nOjoas2fPxpAhQzRtioqK4OrqCoFAgMzMTIwZMwY5OTkGB87qW758Od588ygqK1ffeacCQqEzFIrK\nZq/NHzp0CGlpe9G+fTtMnDiRT51rg4gIw4ePwYEDt1FZ+SzE4l0IC6vEwYN7THIs6O4lR4RCYbMv\n25T0zZsGbQYLCwuRkJAAtVoNtVqNF154AUOGDMHy5csBAImJidi6dSuWLVsGS0tLSCQSbNy40ZBF\nMh1sbW1hYVGAfw4SF8LKStzsZZp1675HYuI7qKycDCurTHz11f/DqVMZsLe3b9Y4WNPKycnBgQO/\norLyCgBrVFa+iBMnAnDy5EmEhoY2ezzmlugby6glHUPwHr5hKioqEBr6KK5e7Y7q6mBIJCvw8cfT\n8fbbrxvcNxHh+++/x6+/ZsLfvzNeffUVnT/dXV19cOPGRgDhAACxeDQWLhyKqVMNP37BWo7z58+j\nd+9hqKi4jNodDIK9fSj27VuOvn37IisrC1VVVQgMDIRIJDJ1uG1Ws+7hs5bD1tYWv/9+EP/5zzIU\nFFzHE08swfDhw43S9+uvv4tVq/ZDLn8BNja/YOPGFBw+vE/rF7mi4jYAb83rmhpv3L592yhxsOah\nVCpRUlKC9u3b6/yF6O/vD29vV2RlvQ6FYhwsLXeifXslunfvjuHDx0AmOwILC1u4udng0KH/wd3d\nvZnXgmllnNP/DdeCQmlzbt++TT///DNlZGSQUqnUe16RSELAzTuDY1RkZxdC+/fv19r+2WcTyMbm\nGQKyCfgficUd6Pjx43ot89KlSxQePoQcHTtS796DKSsrS6/5WeNt2LCJbGwcyNraiTw8/Oj06dM6\n2xYXF9OYMS+Sn18viosbRwUFBbRo0b9JLB5KQBUBarK0fI9GjIhvxjUwL/rmzRaTZTnhN41Lly6R\nm5sPOTgMIDu7bjRw4JNUXV2ts/2pU6do6tTXacqU1+i3336j69evk7W1051L0taOiHRwiKaUlBSt\n81dUVNC4cZOpXTspde78CO3evVuveCsrK8nDw48sLL4k4CpZWCwmNzcfzYhu9o+qqiq9RljXVVNT\nQx9+OIe6du1D4eFRdPjwYbpw4QJJJB0IOHHns15FHh5+pFarH7rfF16YQsDSOqNnj1Hnzj0aFSN7\nME74rJ7IyOFkYfF5nUsoxNDChYu0tj127BjZ2roQ8DEB80kicaFffvmFevUaRCLRKwScIYFgKbVr\n50HFxcVEVHvtcmNek/z48eNkb9+9TsIgcnAIpszMTKMto7VTqVQ0efI0EgqtSSi0pri4sVRVVaWz\nvVqtpnPnztGRI0eorKyMiIimT59BEskgAg4R8B1JJC60cOFCsrcfVe9vb2XlqPmsH8aCBYtILI4m\noPrOHv5MiokZY/A6M+044bN6PD0DCThV50v8b5o06VWtbZ95JoGARXXarqbHH4+jmzdv0siR46lj\nx64UHj6Uzpw5Q0RECxcuISsrW7KwENGgQcPo1q1bBsd7+fJlEotdCSi7E0MFicUd6fz58wb33VYs\nXvwVSSSPElBCgJzE4lh68833tbZVqVQ0duxEEos9yMGhF7m4dKJz586Ro2NHAi5pPmuh8E2aMiWR\nbG27EHD7zvsnyMbGgWpqah46NoVCQVFRcSSReJG9fXfy8Qmi/Px8Y606u4e+eZMP2rZxYWHBuH59\nNWpqFgEoh0SyCf36TdTaVi6vAlB3QJwz5PIqODs7Y/v2dfXa7t27Fx999G8oFH8CkCIjYxoSEl5B\nSsoGg+L18fHB6NFx2L59MCoqhsPWdg+GD49G165dHzyzmdi//zDk8n8BqB3fUFn5On7+eY7Wtps3\nb0ZKyilUVmahslICgWAZnntuMqysrAGUatoJhaXw9w/E2LFW2LAhBEJhMJTKQ1i9+v/pNYhJJBLh\nf//bjnPnzqGqqgpBQUGwtrYGEWHlylXYs+cXdOrkjlmz3kWHDh0M+TOwxmia7Y7+WlAobcr169cp\nKKgvSSQeZG3tRM8//zKpVCqtbbdv304SSac7t5E7QBKJP61evVZr25kzZxEwu86vgSvk5ORhlJjV\najWtX7+ePvjgQ/rvf/+rM15zNW3aWyQSvVpn73yuzgOjs2cnEfBhnc+pkOzsXOjrr/9DEkkXAv5D\nQuE71L69lAoLC4mI6PDhw7R582a6cOGC0WJ+++0PSCIJI2ANiUTTyNPTn0pLS43Wv7nSN2+2mCzL\nCb/pqFQqys7OpmvXrj2w7XffraPAwH7UtWsf+uabFTrbJScnk1g8vM4lln8gf/8wY4bN7lAoFFRY\nWKgprdy4cYM6dw4ke/shZG//FLm4eFF2drbWebds2UK2tiEElBJAZGGxkHr1iiAiom3bttG4cZPp\ntdfeptzc3CaLX6VSkUgkJuCaZsNjZ/cUrV+/vsmWaS444bNmIZfLKTh4ANnZDSRb2/Fka+vS4F4I\ndZ0/f54GDx5Bvr5hNGnSNCovL2/GaFuvtLQ0srNrTzY2LuTk5E4HDx4kIqKysjL64YcfaPPmzXTz\n5k2d86vVanr55dfIxqY92dsHkIeHH128eFGvGNRqNc2d+zl5egZSp06P0IoV/0+v+ZVKJQmFVnWO\nyxDZ2j5Ha9as0asf1hAnfNZsqquraevWrbR69er73jzlxo0b1K6dBwkEiwk4SjY2z9ETT4xsxkhb\np+vXr985a+rgnUSZSg4Orpozbe6lUCgoKWkuDRo0gl566RUqKirSTLty5QqdOnXqvmfz6LJ48ddk\naxtMwO8EHCKJxIe2bNmqVx9jxiSQWPwUAQdJIFhMjo7umhISazxO+KzF2bRpE9nbx9apI1eTpaUN\nn1v/AAcPHiRHx/71TpO0tw+kkydPam3/7LMTSCx+goBtJBK9SV5e3XRuHPQRFjaYgLR6Z2/Fxo7X\nq4+qqip68833qXv3/hQV9TSdO3fO4LgYn6XDWiArKysQleCfC7vV3gnM0tISarUaV69ehUgkgoeH\nh1lfk//333/Hpk0/QCKxwcsvT4JUKkV19QUAhQA6AsiGQlEADw+PBvOWl5dj+/YtUCqLAUhQU/M0\nSkqO4+eff0ZsbKxBcdnb2wIo0LwWCArg6GirVx/W1tZYtGj+gxuyJsX3tGNNLjo6Gh07lsLKaiKA\nFZBIovGvf01DZWUlwsMfR/fuA+DnF4y4uLGoqakxdbgmsW/fPkRExGDBAmvMnXsTPXr0hVAoxIcf\nvguJpBccHOIgFvfDggWfPeAm3XU3mEKjXJBw/vyZkEjeBfARLCxmwM5uCWbOfNPgflnz46tlsmZR\nWlqKL75YhEuX8jBkyABMnjwRL744FZs2KVFdvQKAAhJJLD766Am8/77uG+i0VSEhg3Dy5BsARgEA\nhMIZmD7dAosWfY5Tp04hKysLgYGBDW4hWtfIkeOwd+9tVFZOhaXlr3B1/QHnzx8zyqWpT506hfXr\nN8LSUoiJE1+Er6+vwX0yw/HVMlmL5OjoiLlz6w8O+u23k6iu/hK1PzRtIJePw9GjP5kkPlMrL68A\n8E+pRqXyRGlpFgCgZ8+e6Nmz5wP72Lx5LZKS5uHAga/RpYsXFiw4aLT7EDxsDKxl44TPTKZbN19k\nZe2BUvkYADVsbNLQvXuAqcMyifHjn8aCBW9BLv8GwC1IJAsQH79Grz6srKwwb15Sk8TH2gaDSjpV\nVVWIiIhAdXU1FAoF4uLiMH9+wwMz06dPx549eyCRSLB27Vqtd8Thko75KSgoQP/+Q1BSYg+1Wo6u\nXZ1x8OAe2Nrqd0CwLVCpVJg162N8++1GWFvbYO7c9zFu3FhTh8VauGa9py0AyOVySCQSKJVKPPbY\nY1iwYAEee+wxzfTU1FQkJycjNTUVR48exeuvv46MjAyDA2dtQ2VlJX777TeIRCL06dPngddtodpT\niR9439Tbt29jxYoVuHHjFqKjh+Lxxx83ZtiMtQj65k2Dz9KRSCQAAIVCAZVKBWdn53rTU1JSkJCQ\nAAAIDw9HSUkJioqKDF0sayPEYjEGDRqE/v373zfZExFmz/4UYrEDrK0liI9/CdXV1VrblpWVISTk\nUcyadQxffCHGiBEJWLVKv/IIY22RwQlfrVYjJCQEbm5uGDx4cIOzCPLz8+Hl5aV5LZVKkZeXZ+hi\nmZlZt249FizYhOrqs1Aqi5CSUowZMz7S2nbjxo0oKvJFdfX3AD6CXP4jZsyY1bwBM9YCGXzQ1sLC\nAidOnEBpaSmio6Mhk8kQGRlZr829Pzl0Da5JSkrSPI+MjGzQDzNfu3cfgFz+GoDanYfKyplIS5uu\ntW1ZWRmUSq8673ihsrK86YO8R0VFBRIT38TevfvRvr0Lli9fgEGDBjV7HKztkMlkkMlkjZ7faGfp\nODo64qmnnsLvv/9eL1F7enoiNzdX8zovLw+enp5a+6ib8BmrSyp1hUh0AnfHZQkEJ+Hu7qq1bXR0\nND76KBIKRTSAANjYzMRTT8U1X7B3PP/8FKSlKVFVlYYbN05j2LDROH48na/tzxrt3h3hOXO03wdB\nF4NKOsXFxSgpKQFQe/Bt3759Dc7AiY2NxXfffQcAyMjIgJOTE9zc3AxZLDND77//NtzcfoKtbSwk\nkgmws5uN5GTtQ/WDgoKwc+cG+PvPhovLUIwe7YRvv13WzBEDu3dvR1XVCgBdAYyCWj0Ke/fubfY4\nGLvLoD38wsJCJCQkQK1WQ61W44UXXsCQIUOwfPlyAEBiYiJiYmKQmpoKPz8/2NraYs0aPnjG9Ofi\n4oLTpzOxY8cOKBQKPPnk3HrHhu41dOhQXLjwRzNG2JC1tS1qavJx985UQmE+7Oz6mzQmZt740gqM\nNZGlS7/Bu+9+Brl8CqytT0MqPY0TJw7Dzs4ORASlUgmRSGTqMFkr1uynZTJmStXV1ZgxYxZCQiIw\nYsRYXLp0ydQhabz66r+wbdtyvPVWKT7+OBTHjh2CnZ0dNm/eAgeHDrC2FiM4+FE+a401G97DZ63a\nM89MQGrqTVRWvg0Li0w4OSXjr79OPOCKksZXUFCAb75Zgdu3K/DMM3H1Bh/Wdfr0afTt+zgqK9MA\nBEMo/ARBQftw8mR6s8bL2oZmH2lrLJzwmb4UCgUkEnuoVLcA1F6Owc7uaSxf/izGjRvXbHEUFBSg\nZ89wlJaOhFLZERLJ11i/fhlGjhzZoO3KlSvxxhtHIJevvvOOChYWNqiqknN5h+mNSzrMbFhYWNwZ\n06Go824VhEJhs8bxzTcrUFoaB6XyawAzIZevxYwZn2ht6+bmBguLkwDuXvf/JCQSxwdeUoIxY+CE\nz1otS0tLvPzyVEgkTwFYD5HodTg5XcawYcP06kepVGLVqlWYNesj7NixQ+9fmmVlFVAqO9Z5pyPk\n8gqtbYcPH44BAzrBzq4/JJKJEIufxKpVy8z6Tl+s+XBJh7VqarUaX3/9H+zdewidO3fEnDkz0aFD\nB73mj44ehSNHSlFREQFb2y2YOvVpfPnlpw/dR3p6OqKiRqOyci0AD0gk0/DKKwPx5ZdztbZXqVRI\nTU3FtWvX0L9/fzzyyCMPvSzG6uIaPmN6SE9Px5NPTkZ5+SkAIgDFEIm8UVxcAAcHh4fuZ+fOnZgx\n4xPI5RUYO3Y05s9P4jINa3J8xyvG9HD79m0IhVLUJnsAaA9LS1uUlZXplfDj4uIQF9f8l29gTB+c\n8JlZ69u3L4DTANYCGAqh8Bt06iRFx44dtbYnIvz3v/9FZuYJBAR0wZQpU2BlZdWMETPWeFzSYWbv\n5MmTGD/+X8jNzUZISC9s2LASHh4eWtu+/PJr+P77DMjlYyAW/4S+fS3w88+7HnhDFsaaAtfwGdOB\niPDVV/+MLynMAAAVLElEQVTB+vU74OBgh/nzZ6JPnz4PPf+NGzcglfpBobiK2uvjKGFn9wj27VuL\nfv36NVncjOnCNXzGdJg370vMn/89KirmAcjD4MExOHpUhqCgoIeaXy6XQyi0BXC3tm8JCwtXVFRo\nPwWTsZaGf4cys7F06SpUVKwFEANgCuTyyfj++40PPb+Xlxd8fKQQid4F8BcEgq9gZXVFr18JjJkS\nJ3xmNmrr7Io6rxV6jcq1sLDAgQO7MGRIDtzcnkJ4+C6kp+/T62wexkyJa/jMbCQnL8N77y2CXP5/\nEAjyYGe3GMePH4Gvr6+pQ2OsUfigLWP38f33G7F+/Q44Odnho4/eQUBAgKlDYqzRmjXh5+bmYsKE\nCbh+/ToEAgGmTJmC6dPr31haJpMhLi4OXbp0AQCMHj0as2bNMjhwxhgzd816lo5IJMLixYsREhKC\n8vJy9OrVC1FRUQgMDKzXLiIiAikpKYYsijHGmIEMOmjr7u6OkJAQAICdnR0CAwNRUFDQoB3vuTPG\nmOkZ7SydnJwcHD9+HOHh4fXeFwgEOHz4MIKDgxETE4OzZ88aa5GMMcb0YJSBV+Xl5XjmmWewZMkS\n2NnZ1ZsWFhaG3NxcSCQS7NmzByNHjsSFCxe09pOUlKR5HhkZicjISGOExxhjbYJMJoNMJmv0/Aaf\npVNTU4Phw4dj2LBheOONNx7Y3sfHB3/88QecnZ3rB8IHbRljTC/NeotDIsKkSZPQvXt3ncm+qKhI\nE1BmZiaIqEGyZ4wx1vQMKumkp6dj3bp16NmzJ0JDQwEA8+bNw9WrVwEAiYmJ2Lp1K5YtWwZLS0tI\nJBJs3PjwQ9kZY4wZDw+8YoyxVqpZSzqMMcZaD074jDFmJjjhM8aYmeCEzxhjZoITPmOMmQlO+Iwx\nZiY44TPGmJnghM8YY2aCEz5jjJkJTviMMWYmOOEzxpiZ4ITPGGNmwig3QGGsLaqqqkJGRgYEAgH6\n9esHa2trU4fEmEE44TOmRXFxMfr1exzXr1sDILi7q5CR8RPfy4G1alzSYUyLGTP+D1evRqKsLBNl\nZb/hypV++OCDOaYOizGDGJTwc3NzMXjwYAQFBeGRRx7BV199pbXd9OnT4e/vj+DgYBw/ftyQRTLW\nLM6fv4yammgAAgACKBTROHfusqnDYswgBiV8kUiExYsX48yZM8jIyMDSpUtx7ty5em1SU1Nx8eJF\nZGVlYcWKFZg6dapBATPWHPr3D4WNzRoANQAUEIvXYsCAUFOHxZhBDEr47u7uCAkJAQDY2dkhMDAQ\nBQUF9dqkpKQgISEBABAeHo6SkhIUFRUZsljGmtzcuf+HAQOqYWPTEdbWHTFwoABz5nxo6rAYM4jR\nDtrm5OTg+PHjCA8Pr/d+fn4+vLy8NK+lUiny8vLg5uZmrEUzZnRisRj796egsLAQAoEA7u7uEAgE\npg6LMYMYJeGXl5fjmWeewZIlS2BnZ9dg+r33XOQvDmsNBAIBPDw8TB0GY0ZjcMKvqanB6NGj8fzz\nz2PkyJENpnt6eiI3N1fzOi8vD56enlr7SkpK0jyPjIxEZGSkoeExxlibIZPJIJPJGj2/gPS55fk9\niAgJCQlo3749Fi9erLVNamoqkpOTkZqaioyMDLzxxhvIyMhoGIied19njDFzp2/eNCjhHzp0CIMG\nDULPnj01ZZp58+bh6tWrAIDExEQAwLRp05CWlgZbW1usWbMGYWFhBgfOGGPmrlkTvjFxwmeMMf3o\nmzd5pC1jjJkJTviMMWYmOOEzxpiZ4ITPGGNmghM+Y4yZCU74jDFmJjjhM8aYmeCEzxhjZoITPmOM\nmQlO+IwxZiY44TPGmJnghM8YY2aCEz5jjJkJTviMMWYmOOEzxpiZ4ITPGGNmwuCEP3HiRLi5uaFH\njx5ap8tkMjg6OiI0NBShoaH49NNPDV0kY4yxRjD4JuYvvfQSXnvtNUyYMEFnm4iICKSkpBi6KMYY\nYwYweA9/4MCBaNeu3X3b8K0LGWPM9Jq8hi8QCHD48GEEBwcjJiYGZ8+ebepFMsYY08Lgks6DhIWF\nITc3FxKJBHv27MHIkSNx4cKFpl4sY4yxezR5wre3t9c8HzZsGF555RXcunULzs7ODdomJSVpnkdG\nRiIyMrKpw2OMsVZDJpNBJpM1en4BGaHAnpOTgxEjRuDPP/9sMK2oqAiurq4QCATIzMzEmDFjkJOT\n0zAQgYBr/Ywxpgd986bBe/hjx47FL7/8guLiYnh5eWHOnDmoqakBACQmJmLr1q1YtmwZLC0tIZFI\nsHHjRkMXyRhjrBGMsodvDLyHzxhj+tE3b/JIW8YYMxOc8BljzExwwmeMMTPBCZ8xxswEJ3zGGDMT\nnPAZY8xMcMJnjDEzwQmfMcbMBCd8xhgzE5zwGWPMTHDCZ4wxM8EJnzHGzAQnfMYYMxOc8BljzExw\nwmeMMTPBCZ8xxsyEQQl/4sSJcHNzQ48ePXS2mT59Ovz9/REcHIzjx48bsjjGGGMGMCjhv/TSS0hL\nS9M5PTU1FRcvXkRWVhZWrFiBqVOnGrI4xhhjBjAo4Q8cOBDt2rXTOT0lJQUJCQkAgPDwcJSUlKCo\nqMiQRTLGGGukJq3h5+fnw8vLS/NaKpUiLy+vKRfJGGNMB8umXsC9N9gVCAQ62yYlJWmeR0ZGIjIy\nsomiYoyx1kcmk0EmkzV6/iZN+J6ensjNzdW8zsvLg6enp872dRM+Y4yx+u7dEZ4zZ45e8zdpSSc2\nNhbfffcdACAjIwNOTk5wc3NrykUyxhjTwaA9/LFjx+KXX35BcXExvLy8MGfOHNTU1AAAEhMTERMT\ng9TUVPj5+cHW1hZr1qwxStCMMcb0J6B7i+wmIhAIGtT7GWOM6aZv3uSRtowxZiY44TPGmJnghM8Y\nY2aCEz5jjJkJTviMMWYmOOEzxpiZ4ITPGGNmghM+Y4yZCU74jDFmJjjhM8aYmeCEzxhjZoITPmOM\nmQlO+IwxZiY44TPGmJnghM8YY2aCEz5jjJkJgxN+WloaAgIC4O/vj88//7zBdJlMBkdHR4SGhiI0\nNBSffvqpoYtkjDHWCAbd4lClUmHatGnYv38/PD090adPH8TGxiIwMLBeu4iICKSkpBgUKGOMMcMY\ntIefmZkJPz8/eHt7QyQSIT4+Hjt37mzQjm9dyBhjpmdQws/Pz4eXl5fmtVQqRX5+fr02AoEAhw8f\nRnBwMGJiYnD27FlDFskYY6yRDCrpCASCB7YJCwtDbm4uJBIJ9uzZg5EjR+LChQta2yYlJWmeR0ZG\nIjIy0pDwGGOsTZHJZJDJZI2eX0AG1FsyMjKQlJSEtLQ0AMD8+fNhYWGB9957T+c8Pj4++OOPP+Ds\n7Fw/ED3vvs4YY+ZO37xpUEmnd+/eyMrKQk5ODhQKBTZt2oTY2Nh6bYqKijQBZWZmgogaJHvGGGNN\nz6CSjqWlJZKTkxEdHQ2VSoVJkyYhMDAQy5cvBwAkJiZi69atWLZsGSwtLSGRSLBx40ajBM4YY0w/\nBpV0jIlLOowxpp9mLekwxhhrPTjhM8aYmeCEzxhjZoITPmOMmQlO+E1MrQb+/tvUUTDGmIGnZbIH\nu3YNCAgAhELAxwfo0qX237rPvb0Ba2tTR8oYa+v4tMxmQATcvAlkZ9c+Ll+u/29uLtChg/aNQZcu\nQMeOgAX/FmOM3UPfvMkJvwVQKoH8fO0bg8uXgdJSoHNn7RsDHx/AycnUa8AYMwVO+G2QXA7k5Gjf\nGGRnAyKR7nJR585cLmKsreKEb2aIgOJi3eWivDzA1VV3ucjdnctFjLVWnPBZPUplbdLXVS66fbv2\nV8C9ZaK7/zo6mnoNGGO6cMJneqmo0F4uuvvc2lr3sYPOnQErK1OvAWPmixM+M5q75SJdxw7y8wE3\nN+0bg7vlooe4Rw5jrJE44bNmo1TWnlKqbWOQnQ2UlWkvF9197uBg6jVgrHXjhM9ajPLy+5eLbGx0\nHzvo1InLRYw9CCd81ioQATdu6N4YFBTUloS0bQx8fLhcxBhggoSflpaGN954AyqVCpMnT9Z6P9vp\n06djz549kEgkWLt2LUJDQw0OnLVtNTUNy0V1n5eX116SQtvGwMeHy0XMPDRrwlepVOjWrRv2798P\nT09P9OnTBxs2bEBgYKCmTWpqKpKTk5GamoqjR4/i9ddfR0ZGhsGBM/NWXq57Y5CdDYjFuo8ddOpU\nO1iNsdZO37xp0MXTMjMz4efnB29vbwBAfHw8du7cWS/hp6SkICEhAQAQHh6OkpISFBUVwc3NzZBF\nMzNnZwf06FH7uBcRcP16/Q3A0aPAxo217xUW1l6fSNfoZDc3LhextsmghJ+fnw8vLy/Na6lUiqNH\njz6wTV5eHid81mQEgtqk7eYG9O/fcHpNDXD1av1fBj/++M8GQi6vXy66d8Ngb9/sq8SYURiU8AUP\nuRt0708OXfMlJSVpnkdGRiIyMrKxoTGmk0gE+PrWPrQpK2tYJvrpp3/es7XVfakKLy8uF7GmI5PJ\nIJPJGj2/QQnf09MTubm5mte5ubmQSqX3bZOXlwdPT0+t/dVN+IyZir090LNn7eNeREBRUf2NwZEj\nwPff176+dg3w8NA9OtnVlctFrPHu3RGeM2eOXvMblPB79+6NrKws5OTkwMPDA5s2bcKGDRvqtYmN\njUVycjLi4+ORkZEBJycnLuewVksgqD0l1N1de7lIoag9u6ju6aY7d/7zurJS98bAx6f22ARjTcWg\nhG9paYnk5GRER0dDpVJh0qRJCAwMxPLlywEAiYmJiImJQWpqKvz8/GBra4s1a9YYJXDGWiIrq/uX\ni27frl8uunQJ2Lev9nVOTm3C13WpCi8vwJLvUccMwAOvGGshiGpLQrouVXG3XKRrdHKHDlwuMjc8\n0paxNkqhqD27SNfF7Kqr718usrU19RowY+OEz5iZKi3VfSOcnJza0ce6NgZcLmqdOOEzxhpQq+9f\nLioqAjw9dZeLXFy4XNQSccJnjOmtulp7ueju85oa7YPQ7j6XSEy9BuaJEz5jzOhKSrRfs+jyZeDK\nldpbYeoqF0mlXC5qKpzwGWPNSq2uvT6RrovZXb9em/R1XcyufXsuFzUWJ3zGWItSXV37K0DbxuDy\n5do7p+naGHh7c7nofjjhM8Zalb///mdDcO/G4MoVoF073ccOpFJAKDT1GpgOJ3zGWJuhVtfe/UzX\n6aY3btSeUqrrYnbOzm27XMQJnzFmNqqqan8FaNsYXL4MvPoqMHeuqaNsOpzwGWPsDqWybZ8hpG/e\ntGjCWBhjzKTacrJvDE74jDFmJjjhM8aYmeCEzxhjZqLRFa5bt27hueeew5UrV+Dt7Y3NmzfDycmp\nQTtvb284ODhAKBRCJBIhMzPToIAZY4w1TqP38D/77DNERUXhwoULGDJkCD777DOt7QQCAWQyGY4f\nP262yd6Qmw63Brx+rRuvn/lodMJPSUlBQkICACAhIQE7duzQ2dbcT7ds6//heP1aN14/89HohF9U\nVKS5GbmbmxuKioq0thMIBBg6dCh69+6NlStXNnZxjDHGDHTfGn5UVBSuXbvW4P259wxdEwgEEOgY\nv5yeno6OHTvixo0biIqKQkBAAAYOHGhAyIwxxhqFGqlbt25UWFhIREQFBQXUrVu3B86TlJRECxYs\n0DrN19eXAPCDH/zgBz8e8uHr66tX3m70WTqxsbH49ttv8d577+Hbb7/FyJEjG7SRy+VQqVSwt7dH\nRUUF9u7di9mzZ2vt7+LFi40NhTHG2ENo9LV0bt26hTFjxuDq1av1TsssKCjAyy+/jN27d+Py5csY\nNWoUAECpVGL8+PH44IMPjLoCjDHGHk6LuXgaY4yxpmXSkbZbtmxBUFAQhEIhjh07pnk/JycHYrEY\noaGhCA0NxSuvvGLCKBtP1/oBwPz58+Hv74+AgADs3bvXRBEaT1JSEqRSqeYzS0tLM3VIBktLS0NA\nQAD8/f3x+eefmzoco/P29kbPnj0RGhqKvn37mjocg02cOBFubm7o0aOH5r1bt24hKioKXbt2xRNP\nPIGSkhITRmgYbeun9/dOr4q/kZ07d47++usvioyMpD/++EPzfnZ2Nj3yyCMmjMw4dK3fmTNnKDg4\nmBQKBWVnZ5Ovry+pVCoTRmq4pKQkWrhwoanDMBqlUkm+vr6UnZ1NCoWCgoOD6ezZs6YOy6i8vb3p\n5s2bpg7DaA4ePEjHjh2rlztmzJhBn3/+ORERffbZZ/Tee++ZKjyDaVs/fb93Jt3DDwgIQNeuXU0Z\nQpPStX47d+7E2LFjIRKJ4O3tDT8/vzYxCpnaUHUwMzMTfn5+8Pb2hkgkQnx8PHbu3GnqsIyuLX1m\nAwcORLt27eq9p88A0ZZO2/oB+n2GLfbiadnZ2QgNDUVkZCQOHTpk6nCMqqCgAFKpVPNaKpUiPz/f\nhBEZx9dff43g4GBMmjSpVf90BoD8/Hx4eXlpXreVz6gucxgU+bADRFszfb53TZ7wo6Ki0KNHjwaP\nH3/8Uec8Hh4eyM3NxfHjx7Fo0SKMGzcOZWVlTR1qozRm/bTRNXCtJdG1rikpKZg6dSqys7Nx4sQJ\ndOzYEW+//bapwzVIa/g8DJWeno7jx49jz549WLp0KX799VdTh9Sk7jdAtLXS93vX5PeD2bdvn97z\nWFlZwcrKCgAQFhYGX19fZGVlISwszNjhGawx6+fp6Ync3FzN67y8PHh6ehozrCbxsOs6efJkjBgx\noomjaVr3fka5ubn1fpW1BR07dgQAdOjQAU8//TQyMzPb3Ch4Nzc3XLt2De7u7igsLISrq6upQzKq\nuuvzMN+7FlPSqVuHKi4uhkqlAgBcvnwZWVlZ6NKli6lCM4q66xcbG4uNGzdCoVAgOzsbWVlZrf4s\nicLCQs3z7du31zuToDXq3bs3srKykJOTA4VCgU2bNiE2NtbUYRmNXC7X/Gq+OyiytX9m2twdIApA\n5wDR1kzv752RDyTrZdu2bSSVSsnGxobc3NzoySefJCKirVu3UlBQEIWEhFBYWBjt2rXLlGE2mq71\nIyKaO3cu+fr6Urdu3SgtLc2EURrHCy+8QD169KCePXtSXFwcXbt2zdQhGSw1NZW6du1Kvr6+NG/e\nPFOHY1SXL1+m4OBgCg4OpqCgoDaxfvHx8dSxY0cSiUQklUpp9erVdPPmTRoyZAj5+/tTVFQU/f33\n36YOs9HuXb9Vq1bp/b3jgVeMMWYmWkxJhzHGWNPihM8YY2aCEz5jjJkJTviMMWYmOOEzxpiZ4ITP\nGGNmghM+Y4yZCU74jDFmJv4/cy4YoRUTlN8AAAAASUVORK5CYII=\n", "text": "" } ], "prompt_number": 183 }, { "cell_type": "markdown", "metadata": {}, "source": "The bias allows us to compensate for non-centered data. Let's see how the predictions change once we add it." }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=linear_basis)\nmodel.fit_normal_eqns(X, y,)\nXn = arange(-10, 10, 0.05).reshape((-1,1))\nyh = model.predict(Xn)\nscatter(X, y)\nplot(Xn, yh)\ntitle('Linear basis, with bias')\nshow()", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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E5ZRSJCbOYf78+ZhMJYwePY5Vq96Wk/EqYdGjX7Kzs8nJyQGgoKCATZs2ERERUabN6NGj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\nOU5d2JTMzExWr15NUZGBsWP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"text": "" } ], "prompt_number": 184 }, { "cell_type": "markdown", "metadata": {}, "source": "Let's try a fourier basis." }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=fourier_basis)\nmodel.fit_normal_eqns(X, y)\nXn = arange(-10, 10, 0.05).reshape((-1,1))\nyh = model.predict(Xn)\nscatter(X, y)\nplot(Xn, yh)\ntitle('Fourier basis')\nshow()", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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mSq1uZTDAiy/C3r0QGwvOVb+cao127hx06WL8gLzvvtL7DQbjcP4//oBHHvmM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\nZMn7XLmSzuDBfWVxF1EtyYReQghhQ+R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"text": "" } ], "prompt_number": 185 }, { "cell_type": "markdown", "metadata": {}, "source": "Polynomial basis." }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=polynomial_basis)\nmodel.fit_normal_eqns(X, y)\nXn = arange(-10, 10, 0.05).reshape((-1,1))\nyh = model.predict(Xn)\nscatter(X, y)\nplot(Xn, yh)\ntitle('Polynomial basis')\nshow()", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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73xnqjTfeUKlVUcWrQYxGo5o4cYrS672Vh0e4cnNrpHbs2FGwPz9fqbvvVmrI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\ngIeHB7fddhu//vorYWFhBdu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CCCFMz52lJnWlFJGRkXh6ejJ//vwyTzZhwgSGDRvGqFGj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\nAAAAAElFTkSuQmCC\n", "text": "" } ], "prompt_number": 190 }, { "cell_type": "markdown", "metadata": {}, "source": "Sigmoid basis." }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=sigmoid_basis)\nmodel.fit_normal_eqns(X, y, 0.1)\nXn = arange(-10, 10, 0.05).reshape((-1,1))\nyh = model.predict(Xn)\nscatter(X, y)\nplot(Xn, yh)\ntitle('Sigmoid basis')\nshow()", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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d+PmN4PjxPRVWg60qa3bqjNJKJisLjh+HFi0su5+bBTqYfpCio5fw0ENG/P3H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\nJAQaNrTj4sVHmT27J+np3qx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s2LChzO9xcnLCyckJMM1G9ff35+jRo3To0KG85ZjdrRyf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\nV0opG/L/MgXbf2lMAP0AAAAASUVORK5CYII=\n", "text": "" } ], "prompt_number": 192 }, { "cell_type": "markdown", "metadata": {}, "source": "It loses accuracy over to the left because the basis functions stop at -8. I suspect the same problem will happen with the heavyside function" }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=heavyside_basis)\nmodel.fit_normal_eqns(X, y, 0.2)\nXn = arange(-10, 10, 0.05).reshape((-1,1))\nyh = model.predict(Xn)\nscatter(X, y)\nplot(Xn, yh)\nylim([2,4])\ntitle('Heavyside step function basis')\nshow()", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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VetKxY08uXrxY4PK+vqauZ0lJpkmvr8T69Tv49ttPWL36PY4c+ZXAwEAAsrOh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\nLZaJjY3l5MmTnDhxgvnz5/Pss8/aLOC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"text": "" } ], "prompt_number": 196 }, { "cell_type": "markdown", "metadata": {}, "source": "We can also fit with gradient descent." }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=fourier_basis)\nmodel.fit_gd(X, y, regularization=1e-5, itrs=100, learning_rate=0.1)\nXn = arange(-10, 10, 0.05).reshape((-1,1))\nyh = model.predict(Xn)\nscatter(X, y)\nplot(Xn, yh)\ntitle('Fourier basis, fit with gradient descent')\nshow()\n", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "initial loss: 10.60546158\nfinal loss: " }, { "output_type": "stream", "stream": "stdout", "text": "0.0112470387183\n" }, { "metadata": {}, "output_type": "display_data", "png": 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GA/z3v8Yulfx8qFYNLl409mdOmQLt2hV/rFLw+uvGua537QJHx2s4OjriUEJH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\nDg5mwYIFRZaLjY0lPDyc4OBgWXdUWM0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"text": "" } ], "prompt_number": 201 }, { "cell_type": "markdown", "metadata": {}, "source": "That was fun. Let's do classification.\n\n# Classification #\n\nWe can use the same model for classification - just predict {0,1} instead of a real number." }, { "cell_type": "markdown", "metadata": {}, "source": "Let's try it out" }, { "cell_type": "code", "collapsed": false, "input": "from sklearn.datasets import make_classification\nX,y = make_classification(n_samples=100, n_features=2, n_informative=2, n_redundant=0, \n n_repeated=0, n_classes=2, n_clusters_per_class=1)\n\nscatter(X[:,0], X[:,1], c=['r' if yi == 1 else 'b' for yi in y])\ny = y.reshape((-1,1))", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": "" } ], "prompt_number": 73 }, { "cell_type": "code", "collapsed": false, "input": "def heavyside_basis(x):\n return hstack(tuple(0.5*(sign(x-mu)+1)) for mu in arange(-5,5,0.3))\n\ndef linear_basis(x):\n return hstack((1,x)).ravel()\n\ndef sigmoid_basis(x):\n return hstack(tuple((1+exp(-x-mu))**-1) for mu in arange(-5,5,0.3))\n\ndef polynomial_basis(x):\n return hstack(tuple(x**i for i in range(5)))\n\ndef rbf_basis(x):\n return hstack(tuple(exp(-(x-mu)**2) for mu in arange(-5,5,0.3)))\n\n#some nice plotting code\ndef plot_contour_scatter(model, title_text):\n #sample from a lattice (for the nice visualization)\n x1, x2 = meshgrid(arange(-5,5,0.1), arange(-5,5,0.1))\n Xnew = vstack((x1.ravel(), x2.ravel())).T\n \n Z = model.predict(Xnew).reshape((-1,1))\n \n #plot - contour plot and scatter superimposed\n contourf(arange(-5,5,0.1), arange(-5,5,0.1), Z[:,0].reshape(x1.shape),\n cmap ='cool',levels=[-1e10,0.499,0.5, 1e10])\n colorsToUse= ['r' if yi == 1 else 'b' for yi in y]\n scatter(X[:,0],X[:,1], c=colorsToUse)\n title(title_text)\n show()\n", "language": "python", "metadata": {}, "outputs": [], "prompt_number": 74 }, { "cell_type": "markdown", "metadata": {}, "source": "Now that we got the auxillary work taken care of, the fun part:" }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=linear_basis)\nmodel.fit_normal_eqns(X, y, 0.1)\n#model.fit_gd(X, y, itrs=100, regularization=0.1, learning_rate=0.01)\nplot_contour_scatter(model, 'Linear basis')", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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HF+ZF+IK+H7AIj7u0djoptqHgFtuqrdCuFt+kFa1v+3PN67KtG1h+96V43I+C\nmcGB9WOoKt5LxtA/+A7weIHm+G5GuoBPgY5AFUQlgqfToZb+DkYCmB/gG21nA+2Be8G5mca/fqiW\neih2oeAW26ntwD6e7Z/+A0/FDWD6nizxuttRMOc3NcHdsPdlbP/oUeD/8I28iwEPzpR0YhLr497W\nGsOZiiPOTfPBf6CscBO7Pt9Gxf6NUJWGIzaR5jeOJP3ae63qooQoBbfYRqgE9pHMI/5cVbyXHTn/\nItU1iA5/eANv5VB2fTbB98y3aYJ3PFV7euAtmUhS5ya0vmMs8c3bExXjm/bf9p6/4N6+GUdsPLEN\nQntzCbGO1iqRkBeagQ1l2zby9fCeeEofBFoBo4GLccS+S9dn51Evq0fNsUX/mcG65+bjdf/z0Dul\n4KjPxf8pweGMtqB6qQ1aq0QiTqgGdrX4xi0556XF/O/WC8F7Hr4p7LfirazHnq8/PiK4jegYMA4c\n9t0lGIYDw9BUCjl9+lsjISnUQ7tanYwsYuo3BB7Ft+6IgeFYi7Nu0hHHNej5G6ITN2E47wRexxF3\nOU2vGYkRFWVB1WJ3GnFLSLFLYB+u9YgnWfPElWDeCqzH9HyOe3vWEcc4ExLp/urnbJ75DO7tn5Ny\n3gga9/9/1hQstqfglpBgx8Cu5nDGYDhTMSs3Ae3BfI7COR1pdfsTOKJ+/hWLTmpAm7smWFanhA8F\nt1jKzoFdrWjhLMzKg/gmzfwLqItpgllVCVH6FZPA8+tv1UMPPcT8+fOJiYmhdevWTJs2jaSkpJN/\no0S8cAhsAPeOfPbkfoJvLe2G+Fb5a01ihwuIio23tjgJW37dnLzssstYtWoVK1asoF27dkyYoH8G\nyokFam3sUFGxdzuOmOb4QhugIUZUE1rd9kcry5Iw51dw9+3bF4fD10SPHj0oKCgISFESnsaM8QV3\nOElo1h7f2iLv4puM8y6OuP0ktutmbWES1gJ2Ae7NN9/khhtuCFRzEkbCaYT9S86ERLpMmsfKxwdT\nue96opObcfa4eTgTEq0uTcLYSYO7b9++FBUVHfX++PHjGTBgAADjxo0jJiaGIUOGHLONMYf95rpc\nLlwu15lVK7YSzoF9uHqZ53HBuxvwVpTjiIm1uhyxqZycHHJyck7pWL+nvE+fPp3XXnuNRYsWERcX\nd/QJNOU94kRKYIucTEhOeV+4cCGTJk1iyZIlxwxtiSwKbJHa4deIu23btlRUVJCSkgJAr169ePnl\nl488gUYU/WNRAAAGZklEQVTcEUGhLXK0kBxxr1+/3p9vlzCgwBapfZrWJWdEgS1iHQW3nBYFtoj1\nFNxyShTYIqFD63HLSSm0RUKLRtxyXApskdCk4JajKLBFQpuCW2oosEXsQcEtCmwRm1FwR7AcV/gt\nsyoSCRTcEUqjbBH7UnBHGAW2iP0puCOEAlskfCi4w5wCWyT8KLjDlAJbJHxpynsYUmiLhDeNuMOI\nAlskMii4w4ACWySyKLhtTIEtEpkU3DakwBaJbApuG9EUdREBBbdtaJQtItUU3CFOgS0iv6TgDlEK\nbBE5HgV3iFFgi8jJKLhDhAJbRE6VpryHAIW2iJwOjbgtpMAWkTOh4LaAAltE/KHgrkUKbBEJBAV3\nLVBgi0gg6eZkkCm0RSTQNOIOEgW2iASL3yPuyZMn43A42LNnTyDqsb0xYxTaIhJcfo248/Pz+fjj\nj2nRokWg6rEthbWI1Ba/gnvUqFFMnDiRq666KlD12I4CW0Rq2xkH97x580hPT6dz586BrMc2tDa2\niFjlhMHdt29fioqKjnp/3LhxTJgwgY8++qjmPdM0j9vOmMOGpS6XC5fLdfqVhhCNskUk0HJycsjJ\nyTmlYw3zRIl7HHl5efTp04eEhAQACgoKaNq0Kbm5uaSmph55AsM4YaifyBLXGX1b0CiwReR0LHad\n+feeKDvP6FJJp06d2L59e83rli1b8s0335CSknJmFYY4BbaIhJKAPMdtGEYgmgk5CmwRCUUBCe4N\nGzYEopmQocAWkVCmKe+/oNAWkVCnKe+HKLBFxC4iPrgV2CJiNxEb3ApsEbGriAtuBbaI2F3EBLem\nqItIuIiI4NYoW0TCSVgHtwJbRMJRWAa3AltEwllYBbcCW0QiQVgEtwJbRCKJ7ae8K7RFJNLYdsSt\nwBaRSGW74FZgi0iks01wK7BFRHxCPrgV2CIiRzqjPSdP6wR+7DkpIhKpTpSdtn+qREQk0ii4RURs\nRsEtImIzCm4REZtRcIuI2IyC+zhycnKsLsESkdjvSOwzRGa/w6XPCu7jCJf/wKcrEvsdiX2GyOx3\nuPRZwS0iYjMKbhERmwn6zEmXy8WSJUuCeQoRkbDTu3fv417aCXpwi4hIYOlSiYiIzSi4RURsRsF9\nCiZPnozD4WDPnj1WlxJ0Dz30EJmZmXTp0oWBAweyf/9+q0sKqoULF9KhQwfatm3L008/bXU5QZef\nn88ll1xCx44d6dSpE88//7zVJdUaj8dDdnY2AwYMsLoUvym4TyI/P5+PP/6YFi1aWF1KrbjssstY\ntWoVK1asoF27dkyYMMHqkoLG4/EwYsQIFi5cyOrVq5k1axZr1qyxuqygio6O5i9/+QurVq3iyy+/\n5KWXXgr7PlebMmUKWVlZGIZhdSl+U3CfxKhRo5g4caLVZdSavn374nD4/lr06NGDgoICiysKntzc\nXNq0aUNGRgbR0dEMHjyYefPmWV1WUKWlpdG1a1cA6tatS2ZmJlu3brW4quArKChgwYIFDB8+PCz2\nB1Bwn8C8efNIT0+nc+fOVpdiiTfffJP+/ftbXUbQFBYW0qxZs5rX6enpFBYWWlhR7dq0aRPLly+n\nR48eVpcSdCNHjmTSpEk1gxK7C/mty4Ktb9++FBUVHfX+uHHjmDBhAh999FHNe+Hwf2o4fp/Hjx9f\nc/1v3LhxxMTEMGTIkNour9aEwz+Zz1RJSQmDBg1iypQp1K1b1+pygmr+/PmkpqaSnZ0dNlPeIz64\nP/7442O+n5eXx8aNG+nSpQvg+6dWt27dyM3NJTU1tTZLDLjj9bna9OnTWbBgAYsWLaqliqzRtGlT\n8vPza17n5+eTnp5uYUW1o7KykmuuuYabbrqJq6++2upygu6LL77gvffeY8GCBbjdboqLixk2bBgz\nZsywurQzZ8opycjIMHfv3m11GUH34YcfmllZWebOnTutLiXoKisrzVatWpkbN240y8vLzS5dupir\nV6+2uqyg8nq95tChQ83777/f6lIskZOTY15xxRVWl+G38LjgUwsi5Z/V99xzDyUlJfTt25fs7Gzu\nuusuq0sKGqfTyYsvvki/fv3Iysri+uuvJzMz0+qygmrp0qW8/fbbLF68mOzsbLKzs1m4cKHVZdWq\ncPhd1pR3ERGb0YhbRMRmFNwiIjaj4BYRsRkFt4iIzSi4RURsRsEtImIzCm4REZtRcIuI2Mz/B68s\nkR72I2DWAAAAAElFTkSuQmCC\n", "text": "" } ], "prompt_number": 75 }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=heavyside_basis)\n#model.fit_normal_eqns(X, y, 0.0)\nmodel.fit_gd(X, y, itrs=100, regularization=0.1, learning_rate=0.01)\nplot_contour_scatter(model, 'Heavyside Basis')", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "initial loss: " }, { "output_type": "stream", "stream": "stdout", "text": "0.320790210969\nfinal loss: " }, { "output_type": "stream", "stream": "stdout", "text": "0.0413932329954\n" }, { "metadata": {}, "output_type": "display_data", "png": 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oC7Q5aa2WeA9g3gV8BLQGSsHTiZ2vP0LmR+/S9Y2vCYiq2Js/iPPp4KRIJcjb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\nDqPgFhFxGAW3iIjDKLhFRBzm/wChFgk8LQg7IgAAAABJRU5ErkJggg==\n", "text": "" } ], "prompt_number": 76 }, { "cell_type": "markdown", "metadata": {}, "source": "Note - the heavyside design matrix is singular for this problem, so using the normal equations is futile." }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=polynomial_basis)\nmodel.fit_normal_eqns(X, y, 0.1)\n#model.fit_gd(X, y, itrs=100, regularization=0.1, learning_rate=0.01)\nplot_contour_scatter(model, 'Polynomial Basis (degree 3)')", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": "" } ], "prompt_number": 77 }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=sigmoid_basis)\nmodel.fit_normal_eqns(X, y, 0.1)\n#model.fit_gd(X, y, itrs=100, regularization=0.1, learning_rate=0.01)\nplot_contour_scatter(model, 'Sigmoid Basis')", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": "" } ], "prompt_number": 78 }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=rbf_basis)\n#model.fit_normal_eqns(X, y, .5)\nmodel.fit_gd(X, y, itrs=1000, regularization=0.01, learning_rate=.1)\nplot_contour_scatter(model, 'RBF Basis')", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "initial loss: 0.401877752627\nfinal loss:" }, { "output_type": "stream", "stream": "stdout", "text": " 0.00210904171445\n" }, { "metadata": {}, "output_type": "display_data", "png": 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"text": "" } ], "prompt_number": 79 }, { "cell_type": "markdown", "metadata": {}, "source": "Now how about we modify the basis functions to take interaction between dimensions into account. In other words, instead of $\\phi_i(x_j)$, make $\\phi_i(x_0, ... , x_n)$.\n\nI'll do this by first projecting x into a higher dimensional space of interactions (via a random matrix), and then doing the regular basis functions there." }, { "cell_type": "code", "collapsed": false, "input": "A = uniform(-0.5, 0.5, (10,2))\ndef heavyside_basis(x):\n xn = dot(A,x)\n return hstack(tuple(0.5*(sign(xn-mu)+1)) for mu in arange(-5,5,0.5))\n\ndef linear_basis(x):\n xn = dot(A,x)\n return hstack((1,xn)).ravel()\n\ndef sigmoid_basis(x):\n xn = dot(A,x)\n return hstack(tuple((1+exp(-xn-mu))**-1) for mu in arange(-5,5,0.3))\n\ndef polynomial_basis(x):\n xn = dot(A,x)\n return hstack(tuple(xn**i for i in range(5)))\n\ndef rbf_basis(x):\n xn = dot(A,x)\n return hstack(tuple(exp(-(xn-mu)**2) for mu in arange(-5,5,0.3)))\n", "language": "python", "metadata": {}, "outputs": [], "prompt_number": 80 }, { "cell_type": "markdown", "metadata": {}, "source": "I expect linear models to be the same. Composition of linear functions is linear." }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=linear_basis)\nmodel.fit_normal_eqns(X, y, 0.1)\n#model.fit_gd(X, y, itrs=100, regularization=0.1, learning_rate=0.01)\nplot_contour_scatter(model, 'Linear basis')", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": "" } ], "prompt_number": 81 }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=heavyside_basis)\n#model.fit_normal_eqns(X, y, 0.2)\nmodel.fit_gd(X, y, itrs=100, regularization=0.1, learning_rate=0.01)\nplot_contour_scatter(model, 'Heavyside basis')", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "initial loss: " }, { "output_type": "stream", "stream": "stdout", "text": "1.38533954693\nfinal loss: " }, { "output_type": "stream", "stream": "stdout", "text": "0.0143174964811\n" }, { "metadata": {}, "output_type": "display_data", "png": 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uQmCC\n", "text": "" } ], "prompt_number": 82 }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=sigmoid_basis)\n#model.fit_normal_eqns(X, y, 0.1)\nmodel.fit_gd(X, y, itrs=100, regularization=0.1, learning_rate=0.01)\nplot_contour_scatter(model, 'Sigmoid basis')", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "initial loss: " }, { "output_type": "stream", "stream": "stdout", "text": "0.328485404567\nfinal loss: " }, { "output_type": "stream", "stream": "stdout", "text": "0.0937578444874\n" }, { "metadata": {}, "output_type": "display_data", "png": 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"text": "" } ], "prompt_number": 83 }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=polynomial_basis)\n#model.fit_normal_eqns(X, y, 0.1)\nmodel.fit_gd(X, y, itrs=1000, regularization=0.1, learning_rate=0.01)\nplot_contour_scatter(model, 'Polynomial basis')", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "initial loss: 0.458981318706\nfinal loss:" }, { "output_type": "stream", "stream": "stdout", "text": " 0.0162158979183\n" }, { "metadata": {}, "output_type": "display_data", "png": 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"text": "" } ], "prompt_number": 84 }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=rbf_basis)\n#model.fit_normal_eqns(X, y, 0.1)\nmodel.fit_gd(X, y, itrs=200, regularization=0.1, learning_rate=0.01)\nplot_contour_scatter(model, 'RBF basis')", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "initial loss: " }, { "output_type": "stream", "stream": "stdout", "text": "0.384524839697\nfinal loss:" }, { "output_type": "stream", "stream": "stdout", "text": " 0.0102805578989\n" }, { "metadata": {}, "output_type": "display_data", "png": 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3xJM5uITcqR/RILcvJZvXsPp3N7Jy5BVsn/vqUTcsN8+YCjwMNAIuwxqzvROr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\nAABJRU5ErkJggg==\n", "text": "" } ], "prompt_number": 85 }, { "cell_type": "markdown", "metadata": {}, "source": "# Regularization #\n\nLet's compare how regularization affects the model. Let's make a classification problem:" }, { "cell_type": "code", "collapsed": false, "input": "from sklearn.datasets import make_classification\nX,y = make_classification(n_samples=20, n_features=2, n_informative=1, n_redundant=0, \n n_repeated=0, n_classes=2, n_clusters_per_class=1)\n\nscatter(X[:,0], X[:,1], c=['r' if yi == 1 else 'b' for yi in y])\n", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 95, "text": "" }, { "metadata": {}, "output_type": "display_data", "png": 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zJiEhIQwePNjsKKYrLCxk7NixDBw4kEGDBrF48WKzI5nm7NmzJCYmMnToUAYM\nGMCCBQsa3qHpH8G2jg0bNhhut9swDMOYP3++MX/+fJMTmWffvn3G/v37DYfDYezcudPsOG3u/Pnz\nRmRkpPHVV18ZVVVVRnx8vLF3716zY5ni/fffN3bt2mUMGjTI7Cim+/rrr428vDzDMAzj9OnTRkxM\nTIf9e2EYhlFeXm4YhmFUV1cbiYmJxtatW+sd6zVH9I05AaujiI2NJSYmxuwYptGJdt8aPXo03bt3\nNzuGV+jduzdDhw4FIDg4mLi4OEpKSkxOZR673Q5AVVUVbrebHj161DvWa4r+u+o7AUs6Bp1oJ5dT\nUFBAXl4eiYmJZkcxTU1NDUOHDiUkJISxY8cyYMCAesc2eMJUS/P0BCwracx70VHpRDtpyJkzZ5gy\nZQrPPfccwcHBZscxjY+PD5988gknT55kwoQJuFwuHA7HJce2adFv3LixwddfeuklsrKy2Lx5cxsl\nMs/l3ouOLDQ0lMLCwtrtwsJCwsLCTEwk3qK6upqbb76ZO+64g0mTJpkdxyt07dqVlJQUPv7443qL\n3muWbpxOJ08++STr1q0jMDDQ7Dhew+iA334dPnw4+fn5FBQUUFVVxerVq0lLSzM7lpjMMAxmzZrF\ngAEDmDdvntlxTHX06FFOnDgBQGVlJRs3biQhIaHe8V5T9PWdgNURrV27lvDwcHJyckhJSWHixIlm\nR2pTOtHuW9OnT2fUqFEcOHCA8PBwVqxYYXYk02zbto1XX32VLVu2kJCQQEJCAk6n0+xYpvj666+5\n/vrrGTp0KImJiaSmpjJu3Lh6x+uEKRERi/OaI3oREWkdKnoREYtT0YuIWJyKXkTE4lT0IiIWp6IX\nEbE4Fb2IiMWp6EVELO5/AfRO9MkANtSNAAAAAElFTkSuQmCC\n", "text": "" } ], "prompt_number": 95 }, { "cell_type": "markdown", "metadata": {}, "source": "Now we'll insidiously swap labels." }, { "cell_type": "code", "collapsed": false, "input": "for i in range(5):\n y[i] = 1-y[i]\n \nscatter(X[:,0], X[:,1], c=['r' if yi == 1 else 'b' for yi in y])\ny = y.reshape((-1,1))", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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WlJubSwoQc2H7gZoa5u/dy/nz5/HxcasK29QPD4IzMzMvu49bSzfDhg0jPz+fgoICqqqq\nWLVqFWlpaReNSUtL45VXXgEgJyeHbt26ERwc7M607VpHWheUxps8eTLV0dGMDwzkAV9fUgICeOaF\nF8yOZSmhoaF84uXFuQvbOUDPrl3bVck3l1t/Qh8fHxYvXsz48eNxuVzMnDmT2NhYli5dCkB6ejrJ\nyclkZWURGRlJYGAgy5cvb5Hg7c3x48e55ZZf4HQ6CAzsxqJFTzN9+p1mxxIP0alTJzZ+9BFvvPEG\nR44cYe3o0YwYMcLsWJaSnJzMG+PGMXTjRgbabGx2uXj5tdfMjtUmbIaHHGI25k7m7dmECZN5//0e\nVFU9B+QTEDCBDRveYuTIkWZHE+kwDMNg8+bNlJWVMWLECCIiIsyO5LbGdKeKvo0EBHSnsnI/0BMA\nb++H+P3vuzN//nxzg4lIu9aY7tQlENpI9+49gV0Xtgw6ddpFz549zYwkIh2EjujbSFZWFpMnT8cw\nbsbbO5+IiEq2b38ff39/s6OJSDumpRsPs3v3bpxOJ926dWPy5Ml06tTJ7Egi0s6p6EVELE5r9CIi\noqIXEbE6Fb2IiMWp6EVELE5FLyJicSp6ERGLU9GLiFicil480j//+U/CwwfTs2c46en3c+7cucvv\nJCKXpBOmxON89NFHjB07icrK14Er6dx5DnfeGc3Spc+bHU3E4+iEKWmX3n77XSor04GxQBSVlYv4\nxz/WXm43EamHil48TteuXfDzK/zeM4UEBnYxLY9Ie6elG/E4R44cYfDgRI4du46qqivp3Hkpr7++\nhEmTJpkdTcTj6KJm0m4dPXqUv/71b5w4cYq0tBSuueYasyOJeCQVvYiIxTWmO5t9c/Bjx44xZcoU\nDh48SHh4OH//+9/p1q1bnXHh4eH86Ec/wtvbG19fX3Jzc5s7pYiINEOzP4x98sknSUpKYv/+/Ywd\nO5Ynn3zykuNsNhtOp5O8vDyVvLSpZcteJiYmkZiYRP7612VmxxExTbOXbmJiYsjOziY4OJjS0lLs\ndjtffPFFnXH9+vXjk08+4cc//nHDQbR0Iy3ozTdXMXPmfCoqXgJsBATczYsvPsbtt08zO5pIi2rV\n79GXlZURHBwMQHBwMGVlZfWGGDduHMOGDeOll15q7nQiTfLSS29SUbGAb7+Lfz0VFU/y4osrzY4l\nYooG1+iTkpIoLS2t8/zjjz9+0bbNZsNms13yd2zdupU+ffpw+PBhkpKSiImJYdSoUZccm5GRUfuz\n3W7HbrdfJr7IpQUE+APHvvfMUQIDdSN2af+cTidOp7NJ+7i1dON0OunduzfffPMNY8aMueTSzfdl\nZmYSFBTEgw8+WDeIlm6kBX388cfY7clUVMzl26WbZ3n//XdITEw0O5pIi2rVpZu0tDRWrFgBwIoV\nK5g4cWKdMRUVFZw+fRqA8vJy1q9fz+DBg5s7pUijDR8+nK1bN3DPPYdJTy/jww/Xq+Slw2r2Ef2x\nY8e49dZbOXTo0EVfrywpKeHuu+/m3Xff5auvvuKmm24C4Pz589x+++3Mnz//0kF0RC8i0mQ6YUpE\nxOJ09UoREVHRi4hYnYpeRMTiVPQiIhanohcRsTgVvYiIxanoRUQsTkUvImJxKnoREYtT0YuIWJyK\nXkTE4lT0IiIWp6JvpqqqKo4ePaoLsUm7kZOTw6BB19Cr10+49dZfcOrUKbMjSRtR0TfDokV/Jiio\nO337/oT+/Ydy6NAhsyOJNOjgwYOMG5fK7t33c/jw/7BuHdx888/NjiVtRJcpbqJt27aRlDSFiops\noB9eXgsYMsRBXt4Ws6OJ1Gv58uXMnr2J8vLXLjxzDi+vLpw9W46vr6+p2cQ9ukxxK8jNzcXl+hnw\nE8BGTc0D7Nq1vV38IyUdV2BgIDZbCfDvv6ff4OPjh49Pg7eNFotQ0TdRWFgYPj7bgaoLz3zIFVeE\n1ntzdBFPkJaWRljYafz9bwWeICAgid///r/097aD0NJNE9XU1JCWNpXs7N14efXH5drC2rVvMnbs\nWLOjiTSovLycpUuXUlRUyvXXX8eNN95odiRpAbqVYCupqakhOzubI0eOkJiYyJVXXml2JBHpoFp1\njX716tUMHDgQb29vdu7cWe84h8NBTEwMUVFRLFy4sLnTeRQvLy/GjBnDLbfcopIXEY/X7KIfPHgw\na9as4brrrqt3jMvlYtasWTgcDvbs2cPKlSvZu3dvc6cUEZFmaPZH7jExMZcdk5ubS2RkJOHh4QBM\nnTqVtWvXEhsb29xpRUSkiVr1WzfFxcWEhYXVboeGhlJcXNyaU4qIyA80eESflJREaWlpnecXLFhA\namrqZX95U7+6lZGRUfuz3W7Hbrc3aX8REatzOp04nc4m7dNg0W/YsMGdPISEhFBYWFi7XVhYSGho\naL3jv1/0IiJS1w8PgjMzMy+7T4ss3dT31Z5hw4aRn59PQUEBVVVVrFq1irS0tJaYUkREGqnZRb9m\nzRrCwsLIyckhJSWFCRMmAFBSUkJKSgoAPj4+LF68mPHjxzNgwACmTJmiD2JFRNqYTpgSkSapqKjg\nodmz2bx+Pb2Cg/nDkiUMHz7c7Fgdls6M7cD27dvH/v37iY6Opn///mbHaTUul4stW7Zw+vRprrnm\nGq644gqzI1ne7ZMmcc7h4JGzZ/kU+HVQELm7dtV+jVraloq+g1q06M88/HAmvr5XU129gyeeeIT7\n77/P7Fgtrqqqip+NG0dRXh4hXl58ZrPhyM4mLi7O7GiWVVNTQ2c/P466XARdeO4XAQGMfPZZfvWr\nX5maraPSZYo7oNLSUubN+x2Vlds5dSqLyspcHn74/1NSUmJ2tBa3bNkyXDt28OmZMzhOnWLByZPc\n93PdTKM12Ww2/H19Ofy95w7bbHTu3Nm0THJ5KnqLKSoqws/vKiD8wjNX4ecXTlFRkYmpWsfBr77i\nuooKvC9s24FDFvxzehKbzcbvHnmE/xMQwLPAL/z8ONirF5MmTTI7mjRAdx2wmMjISGpqioBsYDTw\nAS5XIVFRUSYna3nD/+M/eCQwkPTycq4AXvDxYdjVV5sdy/J+M38+Ef37s9nhICIkhOfuv5+goKDL\n7yim0Rq9BW3cuJFJk6ZRU+OLl1c1//jHGyQlJZkdq8UZhsEj8+bxzHPP4e/lRXR0NGs3bqRXr15m\nRxNpM/owtgOrqqqirKyM4OBg/Pz8zI7Tqs6cOUNFRQU9e/bUHZOkw1HRi4hYnL51IyIiKnoREatT\n0YuIWJyKXkTE4lT0IiIWpxOmRMRULpeLpX/5C3nbthExYAD3P/CALqnQwvT1SmnQvn37yMj4A8eO\nnWLatFSmT79T31WXFjXzttvIX7uW2yoqWO/vz/HBg9mwbRs+PjoObQx9j17cUlBQwJAhiZw5MxfD\nCCcg4L/IzEzn17+ea3Y0sYiysjL6X3klxVVVBAIuIC4oiKUOB9dee63Z8doFfY9e3PL6629QWTkF\nw5gPTKOiYiVPPfUns2OJhZw7dw5/b2/+vVDjDXT18uLcuXNmxrIcFb3Uq6amBsPw/d4zvtTU1JiW\nR6wnNDSUqJgYZvn5sQNY4O1NaUCA7ljVwppd9KtXr2bgwIF4e3uzc+fOeseFh4czZMgQEhISGDFi\nRHOnExNMmXIr/v6vAC8A7xIQcCf33fdLs2OJhXh5ebFu0yYqJ05kZr9+fHL99byfk0OXLl3MjmYp\nzV6j/+KLL/Dy8iI9PZ0//vGPDB069JLj+vXrx44dO+jRo0fDQbRG75E+/fRT5s9/nOPHTzF1air3\n33+fPowV8SCN6c5mf6wdExPT6LEq8PYrPj6e995bbXYMEXFDq6/R22w2xo0bx7Bhw3jppZdaezoR\nEfmBBo/ok5KSKC0trfP8ggULSE1NbdQEW7dupU+fPhw+fJikpCRiYmIYNWpU89KKiEiTNVj0GzZs\ncHuCPn36ANCzZ08mTZpEbm5uvUWfkZFR+7Pdbsdut7s9v4iIlTidTpxOZ5P2cfuEqTFjxvD0009z\n9SXu1VlRUYHL5aJLly6Ul5dzww038Oijj3LDDTfUDaIPY0VEmqxVT5has2YNYWFh5OTkkJKSwoQJ\nEwAoKSkhJSUFgNLSUkaNGkV8fDyJiYnceOONlyx5ERFpPboEgohIO6ZLIIiIiIpeRMTqVPQiIhan\nohcRsTgVvYiIxanoRUQsTkUvImJxKnoREYtT0YuIWJyKXkTE4lT0IiIWp6IXEbE4Fb2IiMWp6EVE\nLE5FLyJicSp6ERGLU9GLiFicil5ExOJU9CIiFtfsov/Nb35DbGwscXFx3HTTTZw8efKS4xwOBzEx\nMURFRbFw4cJmBxURkeZpdtHfcMMN7N69m88++4zo6GieeOKJOmNcLhezZs3C4XCwZ88eVq5cyd69\ne90K3BE4nU6zI3gMvRff0XvxHb0XTdPsok9KSsLL69vdExMTKSoqqjMmNzeXyMhIwsPD8fX1ZerU\nqaxdu7b5aTsI/SX+jt6L7+i9+I7ei6ZpkTX6ZcuWkZycXOf54uJiwsLCardDQ0MpLi5uiSlFRKSR\nfBp6MSkpidLS0jrPL1iwgNTUVAAef/xx/Pz8uO222+qMs9lsLRRTRESazXDD8uXLjZEjRxqVlZWX\nfP2jjz4yxo8fX7u9YMEC48knn7zk2IiICAPQQw899NCjCY+IiIjLdrXNMAyDZnA4HDz44INkZ2dz\nxRVXXHLM+fPn6d+/P5s2baJv376MGDGClStXEhsb25wpRUSkGZq9Rj979mzOnDlDUlISCQkJ3Hvv\nvQCUlJSQkpICgI+PD4sXL2b8+PEMGDCAKVOmqORFRNpYs4/oRUSkffCYM2MbewJWR7B69WoGDhyI\nt7c3O3fuNDuOKXSi3bdmzJhBcHAwgwcPNjuK6QoLCxkzZgwDBw5k0KBBLFq0yOxIpjl79iyJiYnE\nx8czYMAA5s+f3/AOTf8ItnWsX7/ecLlchmEYxrx584x58+aZnMg8e/fuNfbt22fY7XZjx44dZsdp\nc+fPnzciIiKMr7/+2qiqqjLi4uKMPXv2mB3LFB988IGxc+dOY9CgQWZHMd0333xj5OXlGYZhGKdP\nnzaio6M77N8LwzCM8vJywzAMo7q62khMTDS2bNlS71iPOaJvzAlYHUVMTAzR0dFmxzCNTrT7zqhR\no+jevbvZMTxC7969iY+PByAoKIjY2FhKSkpMTmWegIAAAKqqqnC5XPTo0aPesR5T9N9X3wlY0jHo\nRDu5nIKCAvLy8khMTDQ7imlqamqIj48nODiYMWPGMGDAgHrHNnjCVEtz9wQsK2nMe9FR6UQ7aciZ\nM2eYPHkyzz//PEFBQWbHMY2XlxeffvopJ0+eZPz48TidTux2+yXHtmnRb9iwocHXX375ZbKysti0\naVMbJTLP5d6LjiwkJITCwsLa7cLCQkJDQ01MJJ6iurqam2++mTvuuIOJEyeaHccjdO3alZSUFD75\n5JN6i95jlm4cDgdPPfUUa9euxd/f3+w4HsPogN9+HTZsGPn5+RQUFFBVVcWqVatIS0szO5aYzDAM\nZs6cyYABA5g7d67ZcUx15MgRTpw4AUBlZSUbNmwgISGh3vEeU/T1nYDVEa1Zs4awsDBycnJISUlh\nwoQJZkdqUzrR7jvTpk1j5MiR7N+/n7CwMJYvX252JNNs3bqV1157jc2bN5OQkEBCQgIOh8PsWKb4\n5ptvuP7664mPjycxMZHU1FTGjh1b73idMCUiYnEec0QvIiKtQ0UvImJxKnoREYtT0YuIWJyKXkTE\n4lT0IiIWp6IXEbE4Fb2IiMX9L/EG9MmIA2UbAAAAAElFTkSuQmCC\n", "text": "" } ], "prompt_number": 96 }, { "cell_type": "markdown", "metadata": {}, "source": "And now let's run a classifier with no regularization" }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=sigmoid_basis)\nmodel.fit_normal_eqns(X, y, 0.0)\nplot_contour_scatter(model, 'Sigmoid basis, no regularization')\nprint 'size of weight vector:', norm(model.w)", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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7uzK4SZPUMHDVUKMauUO7MrhJc9QwcNVQoxq5S7tyjptIQdwlWJTIndqWZ9ykKUoevEqu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\nRU5ErkJggg==\n", "text": "" }, { "output_type": "stream", "stream": "stdout", "text": "size of weight vector: 35016673.5307\n" } ], "prompt_number": 103 }, { "cell_type": "markdown", "metadata": {}, "source": "And again, with regularization" }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=sigmoid_basis)\nmodel.fit_normal_eqns(X, y, 0.9)\nplot_contour_scatter(model, 'Sigmoid basis, with regularization')\nprint 'size of weight vector', norm(model.w)", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ECsPgJiJSGAY3EZHCMLiJiBSGwU1EpDAMbiIihWFwExEpDIObiEhhGNxERArD4CYiUhgG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\n/h9nOLoRIjR45gAAAABJRU5ErkJggg==\n", "text": "" }, { "output_type": "stream", "stream": "stdout", "text": "size of weight vector 0.675961545611\n" } ], "prompt_number": 105 }, { "cell_type": "markdown", "metadata": {}, "source": "So we can see that the regulization pulls the size (l2 norm) of the weight vector to zero, which makes the decision boundary \"less complicated\". It can also be seen as putting a centered gaussian prior on the weight vector. Let's look at regularization in regression. " }, { "cell_type": "code", "collapsed": false, "input": "X = arange(-5, 5, 0.5).reshape((-1,1))\ny = sin(X)\n#now add some corruption\ny[2] += 1\ny[-3] -= 1\ny[5] += 2\ny[7] -= 0.2\ny[15] += 1\ny[10] -= 1\n#plot it\nscatter(X,y)", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 110, "text": "" }, { "metadata": {}, "output_type": "display_data", "png": 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Vsdu2bYOvry+GDRuGVatWiR3HJF577TVYWVmhoqJC7ChG1dEL6CyNlC/402g0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\n", "text": "" } ], "prompt_number": 110 }, { "cell_type": "markdown", "metadata": {}, "source": "Now let's fit two models, with and without regularization." }, { "cell_type": "code", "collapsed": false, "input": "def sigmoid_basis(x):\n return hstack(tuple((1+exp(-x-mu))**-1) for mu in arange(-7,7,0.5))", "language": "python", "metadata": {}, "outputs": [], "prompt_number": 125 }, { "cell_type": "markdown", "metadata": {}, "source": "This model doesn't have regularization." }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=sigmoid_basis)\nmodel.fit_normal_eqns(X, y, 0.0)\nyh = model.predict(arange(-7,7,0.1).reshape((-1,1)))\nplot(arange(-7,7,0.1), yh)\nscatter(X,y)\nylim([-4,2])\nprint 'size of weight vector', norm(model.w)", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "size of weight vector 2.52076671123e+13\n" }, { "metadata": {}, "output_type": "display_data", "png": 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STFitH8Hh6AmbbSouXeqOJUv+xXpY5C4U4BygAJf3WqVWoAD0VPq73bx5A8Cd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\n", "text": "" } ], "prompt_number": 137 }, { "cell_type": "markdown", "metadata": {}, "source": "This is obviously a horrible model - it's just hitting the training points. Even a tiny, nonnegative amount of regularization helps." }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=sigmoid_basis)\nmodel.fit_normal_eqns(X, y, 0.00001)\n#model.fit_gd(X, y, itrs=100, regularization=0.001, learning_rate=0.1)\nyh = model.predict(arange(-7,7,0.1).reshape((-1,1)))\nplot(arange(-7,7,0.1), yh)\nscatter(X,y)\nylim([-4,2])\nprint 'size of weight vector', norm(model.w)", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "size of weight vector 124.134729356\n" }, { "metadata": {}, "output_type": "display_data", "png": 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JE/tg/PhPAPBJO02bAm+/LTikmrp2pQJuiqgPXEvJyUCLFnwDB2MZ/52VlYXXX2+MBw+G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\nRKaogBNCiEz9P8V4vTYPMfpAAAAAAElFTkSuQmCC\n", "text": "" } ], "prompt_number": 138 }, { "cell_type": "markdown", "metadata": {}, "source": "Better. Let's increase the regularization" }, { "cell_type": "code", "collapsed": false, "input": "model = LinearModel(basisfunc=sigmoid_basis)\nmodel.fit_normal_eqns(X, y, 0.01)\n#model.fit_gd(X, y, itrs=100, regularization=0.001, learning_rate=0.1)\nyh = model.predict(arange(-7,7,0.1).reshape((-1,1)))\nplot(arange(-7,7,0.1), yh)\nscatter(X,y)\nylim([-4,2])\nprint 'size of weight vector', norm(model.w)", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "size of weight vector 8.07893778044\n" }, { "metadata": {}, "output_type": "display_data", "png": 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r1k3rMoqUnp4OFxcDcnJq3LjHDc7OdZCamqppXY7i1VeBkBB1JuorrxT8WuvW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\nMcCJiHSKAU5EpFP/D+BlqZ3Q19Q+AAAAAElFTkSuQmCC\n", "text": "" } ], "prompt_number": 140 }, { "cell_type": "markdown", "metadata": {}, "source": "And now we can see how regularization is important for models, espescially when we have a lot of parameters (which my basis function mappings did). " } ], "metadata": {} } ] }